Supporting Participatory Management Planning for Catchment Operationalization with Intuitionistic Fuzzy Sets—A Study in Laspias River, Thrace, Greece

Abstract

Bottom-up management in a catchment scale is deemed the optimal way to avoid conflicts among water users through the participation of stakeholders, strategy co-shaping, and solutions co-creation. Water management cannot be one-dimensional; it demands cross sectoral cooperation. Usually, the difficulty lies in proper stakeholder training and inclusion of their opinions, which should be used in a quantifiable manner in water management. The Laspias River watershed occupies an area of 221.8 km² that includes the River Basin District of Thrace; it is characterized by intense agricultural and industrial activity. To comply with the augmented water needs and pollution loads this research aims to utilize a hybrid intuitionistic fuzzy multi-criteria-based methodology to address respectfully stakeholders’ opinion, this research aims to utilize a hybrid intuitionistic fuzzy multi-criteria-based methodology. It is often difficult to manage planning water management measures as the problems include multiple (conflicting) criteria that are based on stakeholder’s opinions, which are usually imprecise and in a rather qualitative form. This study provides the mathematical tools to reach comprehensive decisions with the public involvement offering a practical solution in an existing problem, that is the proper inclusion of stakeholders’ opinion. The weights are produced based on a stakeholder’s opinion. The alternatives’ ranking is achieved based on the fuzzified intuitionistic version of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), and a hierarchy of mitigation problems is achieved via this novel approach.

1. Introduction

Water, along with its importance for life on the planet, faces intense harvesting, impoundments, pollution, and contamination problems, among others, making the future of this resource insecure and uncertain, especially when considering it from the perspective of climate change [1]. Freshwater ecosystems are threatened by various widespread stressors, such as eutrophication and contamination, that are aggravated by the climate crisis as well as practices such as water harvesting and impoundments [2]. Wetlands, lakes, and temporal waterbodies are rapidly disappearing, So essential and meaningful coordination in water management is required and must be directed towards precise goals. Water managers must therefore act proactively to avoid further losses and cooperate/mobilize more stakeholders and end users.

Water resources management (WRM) is not simply an optimization problem; it requires a systemic approach that implies the involvement of interacting entities, intricate dynamics, and multifaceted elements. Typically, WRM involves many criteria, multiple purposes, many stakeholders, and both structural and not structural measures, among others [3]. The WRM was therefore introduced as an approach where all the system “poles”, meaning resources, environment, and consumers, are harmonically addressed to provide immediate solutions while also sustainably safeguarding the future [4]. Originally, the WRM approach had a typical sub-sectoral approach, dealing mostly with water supply, sanitation, irrigation, and hydropower generation [5]. Therefore, the problem could be reduced to a monocriterion optimization problem based on the axiomatic consideration that the “needs” must be covered. There was often a lack of coordination between sectors, and the environmental requirements were either ignored, or some simple constraints were added within the mathematical formulation.

After 2000, the WRM gradually transformed into Integrated Water Resource Management (IWRM), which is a more environmental approach. Its three major pillars are ensuring equitable access to water resources, enhancing environmental sustainability, and promoting economic efficiency of the resource (including allocations). The notion of IWRM entails an endeavor to comprehensively address and harmonize various technical and social aspects of water utilization and governance. Inevitably, it entails the involvement of stakeholders in some capacity [6]. During the last two decades, stakeholder engagement has received increasing amounts of research attention for designing and implementing solutions to tackle water challenges. The IWRM has introduced stakeholder engagement and adaptivity (among other associated practices) as schemes for novel paradigm management. Nonetheless, the successful implementation of such practices remains a formidable challenge [7]. The participatory approaches, which have the goal of engaging (in an institutionalized approach) the stakeholders, aim to foster a sense of ownership from the design process through the implementation of measures, but has not yet (theoretically) yielded the expected reforms in water management [8]. The importance of “hearing the local voices” is reflected in resolutions from organizations like the World Bank, the UN, and the OECD, or the European Commission (aligned with the Europe 2020 strategy). Good water governance and IWRM are intertwined with stakeholder engagement [9].

Nowadays, new concepts and challenges are incorporated in the IWRM as the adaptation to the Water–Energy–Food–Environment (WEFE) nexus, the extreme phenomena, public participation, and globalization, among others. The largest water-related policy that exists at this time in Europe is the revised 20+ version of the Water Framework Directive (WFD) (2000/60/EC), which introduces a framework for a “basin approach” that also embeds the concept of IWRM paradigm. But even the WFD has raised skepticism due to several issues that may occur trying to reach good status in EU waterbodies since stakeholder engagement is low, and, in most countries, there is a top-down procedure in decision making that usually adopts horizontal measures. The complexity that is inherent within catchments (i.e., covering needs, conflicting water uses, ecological services, and uninterrupted provision) presents a significant barrier to the implementation of the mitigation measures in water uses planning (as in WFD RBMPs), where assessments tend to focus, mainly, on human needs, and therefore fail to recognize the water resource’s sustainability. This highlights the need for knowledge improvement through common technical language to ensure common understanding.

Multicriteria decision making (MCDM) is a valuable tool in water resources management problems since it can incorporate complex and often conflicting goals and objectives and multiple-stakeholders. The MCDM techniques can help decision makers systematically evaluate and rank different options based on multiple criteria, such as cost-effectiveness, environmental impact, social acceptability, and technical feasibility. By considering multiple criteria, MCDM can help decision makers make more informed and transparent decisions since the weights and scores of some criteria can be assessed by using the participation of the stakeholders. The mapping of regional/local stakeholder communities is equally important to establish a common technical language, with attention paid to ensuring inclusiveness and assuring that the needs and roles of stakeholders are recognized. However, there are problematics and challenges which must be addressed, including the qualitative evaluation of the criteria, the existence of multiple stakeholders, the different nature of the criteria, and the inherent uncertainty of the multicriteria problem, among others. There are several “schools” of multicriteria analyses; of them, the distance methods are used frequently since these methods can be understandable to the analyst and have a medium degree of difficulty. These approaches identify ideal and anti-ideal points which are fictitious alternatives in the edges of the decision spaces. They then distinguish the alternatives that are nearest to the ideal and furthest from the anti-ideal [10].

Due to the fact that, by using the fuzziness, uncertainty can be incorporated in the models, and, furthermore, since the fuzzy logic simulates the human reasoning, fuzziness is widely used in multicriteria analysis. In brief, fuzzy set theory [11] generalizes the classical or crisp sense, according to Zimmerman [12] and Kafas [13], into the fuzziness sense that is involved in human language, that is, in human judgment, evaluation, and decisions, although this is not an exclusive list of linguistic social terms. Fuzziness can express the linguistic variables whose values are words or sentences in a natural or artificial language [14]. Apart from these, fuzziness can enable us to express the grey zone of decisions and, furthermore, can provide understandable ways to aggregate different information. Fuzziness, based on the ability to imitate the process of thinking, can generate understandable solutions without ambiguous considerations, like the choice of weights or the aggregation method of objective functions, among others [15,16,17].

After the invention of the intuitionistic fuzzy (IF) set and IF numbers [18,19], the expressions used to describe fuzzy sets were totally changed. A fuzzy set uses only a membership function to indicate the degree of belongingness that a member has in the considered set. The degree of non-belongingness is automatically determined as the complement by using the widely used fuzzy complement [20]. The intuitionistic fuzzy sets overcome this restriction. The inherent uncertainty of many real-world problems can be robustly incorporated by using an intuitionistic fuzzy set (IFS) [18], which is an extension of an ordinary fuzzy set (FS) [11]. The main difference between an IFS and an FS is the representation of hesitancy. More specifically, by using fuzzy sets, the decision can be obtained based on the satisfaction (or dissatisfaction) degree to an alternative by using the membership function and its compliment. However, in the case where the decision maker (DM) uses the IFS, a further hesitation degree can be provided to an alternative that is equal to the difference between the unit and the sum of the membership degree and the non-membership degree. Consequently, the opinion of the DMs can be reflected more comprehensively [21]. In recent years, the field of intuitionistic fuzzy multicriteria methods has exhibited significant potential, as evidenced by its growing prominence, particularly since the year 2009 [22]. The use of an intuitionistic fuzzy set has a great importance in this research since it enables us to use the stakeholder’s opinion and then quantify the information.

Linking the above, regarding stakeholder participation within IWRM with the aid of IFS, the focus lies on the spatial scale of the application since some catchments are more vulnerable than others. Remote areas are generally characterized by low income (the Thrace region is one of the poorest regions in EU) and a lack of river stewardship, non-government organization (NGO) participation, and environmental awareness, factors that are crucial to create stakeholder engagement in decision making. Meanwhile, water shortage, especially in times of climate crisis, usually becomes the main issue, and other problems are neglected. This made our effort larger but more valuable. The eye4water project [23] has invested in seminars/workshops, living labs, newsletters, data and findings presented in open publications, and citizens-to-researchers interactions in a “cluster” type to foster regional water governance, enhance the sustainability of monitoring networks, and create stronger bonds with the society. Through its consulting role, eye4water wishes to support decision making and strategic planning by taking into account the stakeholders’ opinions on pressures and possible solutions, assisting ultimately in two remote rural river basins (Laspias and Lissos) to create resilience and mitigate risk. By activating many forms of two-way communication among participants and utilizing institutional support in the form of facilitation and coordination, the aim of good water governance processes was served.

The aim of this study is to incorporate stakeholders’ opinions to assist operationalization and decision making for participatory integrated water resources management in the remote, rural Laspias river basin. Such a method can address complex issues and provide the basis for mitigation measures hierarchy. Stakeholder groups were identified for collaboration in the form of co-management-based governance arrangement. To this aim, semi-structured interviews were held in key areas within the basin. Intuitionistic fuzzy set was used to incorporate the opinions of the stakeholders concerning the weights and the evaluation of criteria. Next, an intuitionistic distance-based method was applied in order to rank several alternatives under multiple criteria.

2. Materials and Methods

2.1. Description of the Study Area

The Laspias River watershed (code EL12-07) occupies an area of 221.8 km², and it is part of the Nestos river basin that belongs to the River Basin District of Thrace (Figure 1a). To the west of the Laspias river stretches the plain of the Nestos river, while to the east of Laspias, toward the Vistonida lagoon, stretches the plain of Xanthi. The catchment of the Laspias is characterized by plains and natural areas with low vegetation and intense agricultural activity without the presence of an irrigation network that can cover water needs. Thus, irrigation is based on the river’s water and groundwater, all leading to the appearance of important water quality problems [24]. The Mediterranean climate has great seasonality, resulting in contrasting hydrological conditions that, when combined with the actual water (mostly agricultural) needs, typically threaten freshwater habitats due to the high flow variability (which is often intermittent during summer).

A few parts of the Laspias watershed have been characterized as protected areas, while habitat fragmentation, nitrate pollution, and reception of organic load and heavy metals (landfill, WWTP, industries) are observed [25,26,27]. The lowland of the Laspias watershed overlies the groundwater systems of Delta Nestos (EL1200060) and Xanthi-Komotini (EL1200050) (Figure 1c), which have quality problems in the coastal zone due to sea intrusion as a consequence of over-pumping [28,29]. The groundwater system in the study area consists of two aquifers, an upper phreatic to semi-confined aquifer and a lower confined aquifer. Rainfall naturally feeds the upper aquifer through the mechanism of infiltration whilst the recharge through the stream bed percolation of the north hilly area is considerably lower. The lower aquifer largely recharges from River Nestos percolation through buried old stream beds and from lateral groundwater inflows coming from the neighboring Vistonida Lagoon hydrogeological basin [28].

The Laspias river basin can be divided into the areas affected by the river and groundwater and those that are affected only by the groundwater systems. More specifically, the areas of influence of the river and groundwater are delimited from the west by the imaginary line that starts from the settlement of Dekarcho, passes between the settlements of Neo Erasmio and Maggana, and ends at the western part of Maggana beach. The eastern boundary of the area of influence of the Laspias river is the imaginary line that joins the settlements of Melissa and Myrodato and ends at Myrodato beach. In the north, the Laspias river is influential up to the settlements of Kypseli, Exohi, and Magiko. In fact, the farmers are not aware of the river, and their crops are irrigated exclusively with groundwater (Figure 1a,b).

As abovementioned, quality problems in the groundwater are observed in the southern part of the investigated area, which lies between the coastline and the settlement of Maggana; a significant number of small diameter shallow wells and larger diameter deep wells are observed in that area. In the area which is not affected by the river, the problems are related to the quantity of groundwater. In particular, in the settlement of Kypseli, almost all of the shallow wells show very little supply; because of this, farmers group together to dig deep wells as the construction and energy costs are very high per person. Deep wells may offer a greater supply, but their collective use cannot fully cover the irrigation needs of each individual.

It should be mentioned that the water of the Laspias river is recharged with water of better quality from the Nestos river through a network of canals. The central canal passes through the area of the settlement of Olvio. The injection point is located east-southeast of the settlement of Dekarcho. In the area between the settlements of Dekarcho and Maggana, an informal small irrigation network has been developed due to the presence of ditches. There are multiple uses for these ditches as they are not only used as irrigation canals but also as a network for artificial recharge of groundwater, and thus contribute indirectly and directly to the qualitative and quantitative upgrading of groundwater.

The simulation of the Laspias watershed should not be based on a water balance model which considers the groundwater system as a single reservoir. The relevant procedure is governed by high uncertainty for the following reasons: (a) the boundaries of the Laspias watershed are not identical to the boundaries of the groundwater systems, (b) apart from rainfall, the Laspias watershed receives significant amounts of surface water from the Nestos River, and (c) the different lateral hydraulic interconnections of the groundwater system and the significant inflows the from Nestos River to the groundwater system through deep percolation are not taken into account in the widely-used, simplified water-basin-based balance used to estimate the water yield (Figure 2).

2.2. Opinion Research

2.2.1. Stakeholders Involvement

Motivational drivers from the scientific part were (a) the participation of local population representatives, (b) spatial extent, in reaching villages that are in close range with the river (within the basin) and (c) the addressing all stakeholder groups that (in our opinion) can contribute to the river amelioration. To manage the participation, designated researchers met the representatives at their workplaces, their fields, and local cafes, and persuade them that their opinion mattered. The project enablers, such as the social media pages and the website, contributed significantly. From the volunteers’ perspective, their major motivations were that their opinions were heard, and they had the opportunity to co-shape solutions that fit them, state their discomfort towards the managing authorities, and provide a contribution to science.

The campaign for stakeholders’ opinions on management practices had a duration of 5 days in May 2022. In-situ research was held in the form of semi-structured interviews based on a questionnaire where an open discussion between the researchers and stakeholders took place. The questionnaire was based on queries with qualitative and natural responses. In total, 41 stakeholders were interviewed; 29 of them were farmers and citizens who occasionally worked in agriculture and 12 were experts. The experts include both practitioners (workers in competent services/bodies, water corporations, and local authorities), as well as academic and research members of the D.U.Th. The primary objective was to ensure that the questions posed were uncomplicated and easily comprehensible, thus enabling individuals with only rudimentary education to provide their valuable insights. The intention was to inclusively incorporate the opinions of diverse respondents. The primary method employed for data collection was oral interviews, with an average interview duration of 40 min allocated per participant, meticulously gauging the perceptions of individuals pertaining to the judicious administration of the river.

The quota of the participant groups was selected in order to counterbalance the linguistic terms for assessing the weightiness of stakeholders and to guarantee the proper inclusion of people with different experience. In other words, the questionnaire-based interviews were chosen to contribute to the development of the multicriteria model by taking into account the experience and expertise of the stakeholders in the case study. Personal data concerning age, educational level, basic employment/occupation, and experience were initially recorded. Then, a set of 10 questions was formed that dealt with problems within the basin, provision services by the river, activities creating pressure, intervention needs (surface water and aquifers), cultivation practices, crop selection, criteria, applicable measures’ importance, and ways to attract young people (growth and decentralization). The nature of the questions and the questions themselves are presented more analytically in Appendix B (

Table A5. Questions from the semi-structure interviews.

Nature of Questions	Interview Questions	Explanations
Individual information	Name	Marking the class belonging to
	Age	Marking the class belonging to
	Knowledge and experience	Marking the class belonging to
	Education level	Marking the class belonging to
Problems and services of surface waters and groundwaters	Q1: What do you think are the main problems regarding the Laspias river basin? Rank from 1 to 8 from the most important to the least important problem.	Citation of a series of problems regarding the quality and quantity of both the surface water and groundwater
	Q2: What do you think are the most important ecosystem services/uses of Laspias River? Rank from 1 to 9 from the most important to the least important service/use.	Citation of a series of services/uses
	Q3: Which of the above ecosystem services do you think could contribute economically in the future?	Notation of one of the ecosystem services cited in the previous question
	Q4: What activities are those that burden the Laspias River?	Citation of a series of activities. Possibility of selection more than one activity
Suggestion and incentives	Q5: Do you think that the Laspias River needs any intervention? Justify your answer.	Free text answer
	Q6: Do you think that the aquifers need any intervention? Justify your answer.	Free text answer
	Q7: In the case you are farmer based on which factor do you choose the type of crop you grow?	Citation of a series of factors
Qualitative assessment of the proposed alternatives and criteria	Q8: How would you assess the importance of the criteria as concern the rational and conjunctive management of groundwater and surface water in the basin of the Laspias River?	Citation of a list of criteria and of a qualitative scale of criteria’s importance
	Q9: Characterize the following alternatives as concern the rational and conjunctive management of groundwater and surface water in the basin of the Laspias	Citation of a list of alternatives (proposed mitigation measures) and of a qualitative scale of alternatives’ importance
	Q10: Characterize the following alternatives regarding attracting new people for residence and employment	Citation of the list of alternatives and of a qualitative scale

). However, it should be noted that the main question of this process from a mathematical point of view, apart from the recognition of the problems, is the assessment of the weights of the criteria.

2.2.2. Criteria Identification

The selection of appropriate criteria is one of the most important steps in water resources management, and the criteria depend on the physical, natural, and socio-financial characteristics of the study area and data availability. However, it is also desired that their number be minimal in order to reduce complexity. Ten criteria encompassing the properties of the given watershed were identified. These are financial, social, and environmental, and address water needs, resilience to climate change, local acceptance and expertise at the prefecture level, the importance of measures, water saving, synergy with other measures, and attracting young people to the countryside to live and work.

Financial criterion: It is one of the three general criteria and refers to the cost of construction, operation, and, more generally, to the cost of implementation and maintenance of a proposed measure (alternative).

Social criterion: It is the second general criterion and refers to the development and welfare of local society caused by a suggested measure.

Environmental criterion: The last general criterion refers to the environmental degradation/upgrading of the local conditions due to the implementation of a proposed measure.

Covering water needs criterion: It focuses on satisfying the water needs of all stakeholders, mainly in quantitative terms.

Resilience to climate change: Every proposed measure is assessed regarding its resilience to climate change, for instance, an increase in the frequency of extreme hydrological events should be taken into account.

Local acceptance and expertise criterion: This criterion ensures the sustainability of the measure over time. Obviously, a measure proposed should be initially acceptable from the local societies, and local authorities should have sufficient expertise to subsequently operate and maintain it.

Importance of measure criterion: This criterion refers to the part of the water body affected by the proposed measure.

Water saving criterion: It refers to measures that could save water by collection and reuse, such as reuse of biologically treated effluents.

Synergy with other measures: to be combined with other measures. For instance, the water from an irrigation network can be used to fill basins/ditches for an artificial recharge of groundwater.

Attracting young people to the countryside to live and work criterion: This measure was included to assess stakeholder opinions regarding the employment of young people in the primary sector.

2.2.3. Proposed Alternatives

As aforementioned, the output of this research is the ranking of the alternatives (i.e., the measures proposed) in terms of their effectiveness in the rational management of the water resources of the Laspias watershed. The preparation of the alternatives was based on the experience of the local conditions, and each alternative was evaluated based on the above ten criteria: (i) reuse waste water (A₁), (ii) inflow of Laspias river from surplus water in the canals (A₂), (iii) changing crops to less water-intensive types (A₃), (iv) establishment of a centralized irrigation network (A₄), (v) grant/use of automation in the irrigation activities (A₅), (vi) artificial recharge of groundwater by utilizing excess water (a) based on flood basin (A₆) and (b) based on ditch network (A₇), (vii) intensification of irrigation (A₈), (viii) no change to the existing situation (A₉), (viii) redesign of production lines and internal recycling of water flows (A₁₀), (ix) removal/deactivation of pollutants (A₁₁), (x) strict implementation of the pricing policy on water use (A₁₂), (xi) strict implementation of the pollution pricing policy (A₁₃), and (xii) monitoring of system pollutants (A₁₄).

Figure 3 illustrates the flow of the implementation of the proposed methodology. Once the primary data (which were of a qualitative nature) were collected (by including the stakeholders’ opinions in the assessment of the alternatives to the criteria), the methodological synthesis was carried out through multi-criteria decision analysis via intuitionistic fuzzy approach. In particular, an intuitionistic fuzzy version of the well-known TOPSIS method was applied, as presented in Section 2.3.

2.3. Methodology Implementation Using MCDA and IFSs

2.3.1. Fundamentals of Intuitionistic Fuzzy Sets

A fuzzy set A in X = {x} is given by A = {(x, μ_A(x)) x ∈Χ} where μ_A:X → [0, 1] is the membership function of the fuzzy set A. As μ_A(x) ∈ [0, 1], the membership of x ∈ X in A is denoted.

On the other hand, an intuitionistic fuzzy set (IFS) A in X = {x} is defined as A = {(x, μ_A(x), x, ν_A(x)) x ∈Χ} where μ_A:X → [0, 1] and ν_A:X → [0, 1] [18] with the condition

0 ≤ μ_A(x) + ν_A(x) ≤ 1, ∀x ∈ Χ

(1)

The terms μ_A(x), ν_A(x) ∈ [0, 1] denote the degree of membership and degree of non-membership, respectively, of an element x to the set A. The number

π_A(x) = 1 − (μ_A(x) + ν_A(x))

(2)

is called the intuitionistic index of x in A. It is a measure of the degree of hesitancy of element x in set A [18]. It should be noted that

0 ≤ π_A(x) ≤ 1 for each x ∈ Χ

(3)

Different relations and operations are introduced over the IFS’s, and some of them are shown in Equations (4)–(7).

$$\begin{array}{cc}A\otimes B=\left\{\right(x, {\mu }_A\left(x\right)·{\mu }_B\left(x\right), {\nu }_A\left(x\right)+{\nu }_B\left(x\right)-{\nu }_A\left(x\right)·{\nu }_B\left(x\right)) x \in {\rm X}\}& \end{array}$$

(4)

$$A\oplus B=\left\{\right(x,{\mu }_A\left(x\right)+{\mu }_B\left(x\right)-{\mu }_A\left(x\right)·{\mu }_B\left(x\right),{\nu }_A\left(x\right)·{\nu }_B\left(x\right)) x \in {\rm X}\}$$

(5)

$$\lambda A=\left\{\right(x, 1-{(1-{\mu }_A\left(x\right))}^{\lambda }), {\left({\nu }_A\left(x\right)\right)}^{\lambda } x\in {\rm X}\}$$

(6)

$$A^{\lambda }=\left\{\right(x,{ \left({\mu }_A\right(x\left)\right)}^{\lambda }, 1-{(1-\left({\nu }_A\left(x\right)\right)}^{\lambda } x\in {\rm X}\}$$

(7)

where λ is a positive integer.

2.3.2. Measuring the Distance and the Similarity between Intuitionistic Fuzzy Sets

The comparison between intuitionistic fuzzy sets can be expressed either through the concept of distance or the concept of similarity. Distance measures between IFSs have gathered a great deal of attention due to their practical applicability in the real world (pattern recognition, machine learning, decision making, and market prediction), making it an important content in fuzzy mathematics.

Based on the geometric interpretation of IFSs Szmidt and Kacprzyk [30] proposed the following normalized distance measure (Equation (8)).

Let $\tilde{A}=\{〈x_i,{\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right)〉\mathrm{x}\in \mathsf{{\rm X}}\}$ and $\tilde{B}=\{〈x_i,{\mu }_{\tilde{B}}\left(x_i\right),{\nu }_{\tilde{B}}\left(x_i\right)〉\mathrm{x}\in \mathsf{{\rm X}}\}$ be two IFS in X = {x₁, x₂, …, x_n}

$$d_{(A,B)}=\sqrt{\frac{1}{2n}\sum _{i=1}^n[{\left(\left|{\mu }_A\left(x_i\right)-{\mu }_B\left(x_i\right)\right|\right)}^2+{\left(\left|{\nu }_A\left(x_i\right)-{\nu }_B\left(x_i\right)\right|\right)}^2+{\left(\left|{\pi }_A\left(x_i\right)-{\pi }_B\left(x_i\right)\right|\right)}^2]}$$

(8)

The measurement of similarity in IFSs is a fundamental concept utilized in various fields of study. The selection and application of appropriate similarity measure depend on the specific requirements and objectives of the problem domain, aiming to provide accurate and meaningful assessments of similarity in IFSs [31].

In this section, the similarity measure between IFSs is based on the centroid points of transformed right-angled triangular fuzzy numbers proposed by Chen [32] to overcome the drawbacks of the existing similarity measures as “the division by zero problem” [33,34,35].

Let $\tilde{A}=\{〈x_i,{\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right)〉1\le i\le n\}$ be an IFS in the universe of discourse X, where $X=\{X_1,X_2\dots ,X_n\}$. Let ${\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right)$ denote the intuitionistic fuzzy value of element $x_i$ belonging to the intuitionistic fuzzy set $\tilde{A}$, where $1\le i\le n$.

Axi is the transformed into a right-angled triangular fuzzy number in the universe of discourse Z = [0, 1] obtained from the intuitionistic fuzzy value ${\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right)$ with the three points $T_{Axi}={(\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right)+{\pi }_{\tilde{A}}\left(x_i\right))$, $U_{Axi}={(\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right))$, and $V_{Axi}={(\mu }_{\tilde{A}}\left(x_i\right)+{\pi }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right))$, where the distance $\overline{T_{Axi}{U}_{Axi}}$ between the points $T_{Axi}{\&U}_{Axi}$ on the Y-axis is equal to ${(\nu }_{\tilde{A}}\left(x_i\right)+{\pi }_{\tilde{A}}\left(x_i\right)-{\nu }_{\tilde{A}}\left(x_i\right))={\pi }_{\tilde{A}}\left(x_i\right)$, the distance $\overline{T_{Axi}{V}_{Axi}}$ between the points $T_{Axi}{\&V}_{Axi}$ on the Z-axis is equal to ${(\mu }_{\tilde{A}}\left(x_i\right)+{\pi }_{\tilde{A}}\left(x_i\right)-{\mu }_{\tilde{A}}\left(x_i\right))={\pi }_{\tilde{A}}\left(x_i\right)$, and the centroid point $C_{Axi}$ of the transformed right-angled triangular fuzzy number $A_{xi}$ is shown as follows (Figure 4):

$$C_{Axi}=\left({(\mu }_{\tilde{A}}\left(x_i\right)+\frac{{\pi }_{\tilde{A}}\left(x_i\right)}{3},{(\nu }_{\tilde{A}}\left(x_i\right)+\frac{{\pi }_{\tilde{A}}\left(x_i\right)}{3}\right)$$

(9)

Since

${\pi }_{\tilde{A}}\left(x_i\right)=1-{\mu }_{\tilde{A}}\left(x_i\right)-{\nu }_{\tilde{A}}\left(x_i\right)$, derives the following

$$\begin{array}{ll}{C}_{Axi}=({(\mu }_{\tilde{A}}\left(x_i\right)& +\frac{{\pi }_{\tilde{A}}\left(x_i\right)}{3},{(\nu }_{\tilde{A}}\left(x_i\right)+\frac{{\pi }_{\tilde{A}}\left(x_i\right)}{3})\\ & =\left(\frac{1+2{\mu }_{\tilde{A}}\left(x_i\right)-{\nu }_{\tilde{A}}\left(x_i\right)}{3},\frac{1+2{\nu }_{\tilde{A}}\left(x_i\right)-{\mu }_{\tilde{A}}\left(x_i\right)}{3}\right)\end{array}$$

(10)

Let $A_{xi}$ and $B_{xi}$ be two right-angled triangular fuzzy numbers transformed from the intuitionistic fuzzy values ${(\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right))$ and ${(\mu }_{\tilde{B}}\left(x_i\right),{\nu }_{\tilde{B}}\left(x_i\right))$ of element $x_i$, as shown in Figure 4, where the centroid points $C_{Axi}$ and $C_{Bxi}$ of the transformed right-angled triangular fuzzy number $A_{xi}$ and $B_{xi}$ shown in Figure 4 are as follows:

$$C_{Axi}=\left(\frac{1+2{\mu }_{\tilde{A}}\left(x_i\right)-{\nu }_{\tilde{A}}\left(x_i\right)}{3},\frac{1+2{\nu }_{\tilde{A}}\left(x_i\right)-{\mu }_{\tilde{A}}\left(x_i\right)}{3}\right)$$

(11)

$$C_{Bxi}=\left(\frac{1+2{\mu }_{\tilde{B}}\left(x_i\right)-{\nu }_{\tilde{B}}\left(x_i\right)}{3},\frac{1+2{\nu }_{\tilde{B}}\left(x_i\right)-{\mu }_B\left(x_i\right)}{3}\right)$$

(12)

Based on Figure 4, the degree of similarity S($A_{xi},B_{xi})$ between the intuitionistic fuzzy values ${(\mu }_{\tilde{A}}\left(x_i\right),{\nu }_{\tilde{A}}\left(x_i\right))$ and ${(\mu }_{\tilde{B}}\left(x_i\right),{\nu }_{\tilde{B}}\left(x_i\right))$ is calculated as follows:

$$\begin{array}{ll}{S(A}_{xi},B_{xi})=1-& \frac{\left|2({\mu }_{\tilde{A}}\left(x_i\right)-{\mu }_{\tilde{B}}\left(x_i\right))-\left({\nu }_{\tilde{A}}\left(x_i\right)-{\nu }_{\tilde{B}}\left(x_i\right)\right)\right|}{3}\\ & \ast \left(1-\frac{{\pi }_{\tilde{A}}\left(x_i\right)+{\pi }_{\tilde{B}}\left(x_i\right)}{2}\right)\\ & -\frac{\left|2{(\nu }_{\tilde{A}}\left(x_i\right)-{\nu }_{\tilde{B}}\left(x_i\right))-\left({\mu }_{\tilde{A}}\left(x_i\right)-{\mu }_{\tilde{B}}\left(x_i\right)\right)\right|}{3}\\ & \ast \left(\frac{{\pi }_{\tilde{A}}\left(x_i\right)+{\pi }_{\tilde{B}}\left(x_i\right)}{2}\right)\end{array}$$

(13)

Chen et al. [36] prove that the proposed similarity measures satisfy the axiomatic definition of the similarity measure S between intuitionistic fuzzy sets. Other advantages of this measure based on its physical meaning can be found in the same sources.

Due to the key role that the measures (some based on the concept of distance and others based on the concept of similarity) play in applying the multicriteria methods, both of these concepts are used. However, the use of similarity measure proposed by [36] is slightly preferred because it gives more balanced (centripetal) solutions, and, furthermore, it overcomes “the division by zero problem”, as abovementioned.

2.3.3. Information Quantification and Synthesis via Intuitionistic Fuzzy Operator

As described below in further detail, in order to quantify the information and combine the aspects of the stakeholders regarding either the scores of the alternatives or the weights of the criteria, an operator based on the principles of intuitionistic fuzzy sets is used. This is the intuitionistic fuzzy weighted averaging (IFWA) operator [37].

Indeed, several researchers have recently concentrated on the topic of aggregation techniques pertaining to intuitionistic fuzzy information [38,39,40]. They put emphasis on defining the concept of IFNs and developing a method that can rank these IFNs based on the functions of their score and accuracy. Apart from the definition of IFNs, they have determined an operational system of laws and imported a series of operators in order to aggregate intuitionistic fuzzy information. The intuitionistic fuzzy weighted averaging operator (IFWA) presented in this study is one of these operators [37].

Let $w_j^{\left(k\right)}=\{{\mu }_j^{\left(\kappa \right)},{\nu }_j^{\left(\kappa \right)},{\pi }_j^{\left(\kappa \right)}$} be an intuitionistic fuzzy number assigned to criterion $x_j$ by k-th DM. Then, the weights of the criteria are computed using the IFWA operator.

$$\begin{array}{l} w_j=IFWA\left(w_j^{\left(1\right)},w_j^{\left(2\right)},\dots ,w_j^{\left(k\right)},\dots ,w_j^{\left(l\right)}\right)\\ ={\lambda }_1{w}_j^{\left(1\right)}\oplus {\lambda }_2{w}_j^{\left(2\right)}\oplus \dots \oplus {\lambda }_{\kappa }{w}_j^{\left(k\right)}\oplus \dots \oplus {\lambda }_l{w}_j^{\left(l\right)}\\ =[1-\prod _{k=1}^l{\left(1-{\mu }_j^{\left(\kappa \right)}\right)}^{\lambda \kappa },\\ \prod _{k=1}^l({{\nu }_j^{\left(\kappa \right)})}^{\lambda \kappa },\prod _{k=1}^l{\left(1-{\mu }_j^{\left(\kappa \right)}\right)}^{\lambda \kappa }-\prod _{k=1}^l({{\nu }_j^{\left(\kappa \right)})}^{\lambda \kappa },]\end{array}$$

(14)

where $w_j=\{{\mu }_j,{\nu }_j,{\pi }_j\}$.

The above equation is based on Equations (4) and (6), and this operation produced also an intuitionistic fuzzy value. Where $\lambda$ is the corresponding weight of k-th stakeholders or, more generally, the people who participate in the research, it can be obtained by using the following equation proposed by [41]:

$${\mathsf{\lambda }}_{\mathsf{\kappa }}=\frac{({\mathsf{\mu }}_{\mathsf{\kappa }}+{\mathsf{\pi }}_{\mathsf{\kappa }}\ast \left(\frac{{\mathsf{\mu }}_{\mathsf{\kappa }}}{{\mathsf{\mu }}_{\mathsf{\kappa }}+{\nu }_{\mathsf{\kappa }}}\right))}{{\sum }_{\mathrm{k}=1}^{\mathrm{l}}({\mathsf{\mu }}_{\mathsf{\kappa }}+{\mathsf{\pi }}_{\mathsf{\kappa }}\ast \left(\frac{{\mathsf{\mu }}_{\mathsf{\kappa }}}{{\mathsf{\mu }}_{\mathsf{\kappa }}+{\nu }_{\mathsf{\kappa }}}\right))}$$

(15)

the values μ_κ, ν_κ, π_κ can be taken from

Table 1. The final criteria’s weights derived as fuzzy intuitionistic information.

Criteria	IFN (μ, ν, π)
1. Financial	0.8329	0.1303	0.0368
2. Social	0.7280	0.1769	0.0951
3. Environmental	0.7918	0.1591	0.0490
4. Covering water needs	0.7706	0.1606	0.0688
5. Resilience of measures to climate change	0.7245	0.1823	0.0932
6. Local acceptance and expertise at the prefecture level	0.7208	0.2033	0.0759
7. Importance of the measure	0.6896	0.2122	0.0982
8. Saving water	0.7297	0.1853	0.0850
9. Synergy with other measures	0.6632	0.2376	0.0992
10. Attracting new people to the countryside to live and work	0.6956	0.2174	0.0869

.

Since there are weights, the symmetry property in Equation (14) does not hold. However, regarding the membership function μ, this aggregator is near to the fuzzy union since if at least one stakeholder proposes ${\mu }_j^{\left(\kappa \right)}=1,then {\mu }_j=1.$ This fact reminds us to the use of the boundary condition in this case, the fuzzy union.

To acquire this information, the completion of the questionnaires and interviews are necessary as the education, training, and experience of the respondents themselves have been noted. The questionnaires included qualitative terms that were converted into intuitionistic fuzzy values, these values are based on [42]. Therefore, the linguistic terms for rating the stakeholders are, Beginner, Practitioner, Proficient, Expert and Master and the IFN’s are {0.10, 0.90, 0.00}, {0.35, 0.60, 0.05}, {0.50, 0.45, 0.05}, {0.75, 0.20, 0.05} and {0.90, 0.10, 0.00} respectively. For instance, if the linguistic term expressing the importance of stakeholders is either beginner or expert the degree of hesitancy π is equal to zero.

In the second step, the participants were invited to answer how they would judge the importance of the criteria for the rational use of the Laspias river. Which again was done in verbal terms and turned into intuitionistic fuzzy values. The linguistic terms that were adopted by [41] are, [Extremely Bad/Extremely Low], [Very Bad/Very Low], [Bad/Low], [Medium Bad/Medium Low], [Fair/Medium], [Medium Good/Medium High], [Good/High], [Very Good/Very High], [Excellent/Extremely High] and the IFN’s are {0.1, 0.9, 0}, {0.1, 0.75, 0.15}, {0.25, 0.6, 0.15}, {0.4, 0.5, 0.1}, {0.5, 0.4, 0.1}, {0.6, 0.3, 0.1}, {0.7, 0.2, 0.1}, {0.8, 0.1, 0.1}, {0.8, 0.1, 0.1}, {0.9, 0.1, 0.0} respectively. However, the authors have slightly modified them because as aforementioned, if one value is equal to one the result of IFWA regarding the membership equals one. By the same way the participants can evaluate some kind of criteria. These values show the conversion into intuitionistic fuzzy values.

2.3.4. Applied Intuitionistic Fuzzy TOPSIS Using Similarity Measure

TOPSIS, which was developed by [43], is based on the idea that the chosen alternative should have the shortest distance from the positive ideal solution and simultaneously the longest distance from the negative ideal solution. Let A = {A₁, A₂, …, A_m} be a set of alternatives and X = {X₁, X₂, …, X_n} be a set of criteria, the procedure for Intuitionistic Fuzzy TOPSIS method has been given as follows:

Step 1. Determine the weights of each participant. Assume that participants contributed to the investigation. The importance of each participant was calculated with respect to the abovementioned scale [37], that is, by considering the educational level and the experience. Then the weight of each participant can be obtained as a crisp value by using the Equation (15).

Step 2. Aggregate all information based on the participants by using the IFWA operator (Equation (14)). In this application, these steps mainly concern the weights of the criteria. W denotes a set of grades of importance. The weights of the criteria are also computed using Equation (14).

Step 3. Construct intuitionistic fuzzy decision matrix for each criterion and alternative A_j by transforming the opinions of experts into Intuitionistic Fuzzy Values.

$$R=\left[\begin{array}{cccc}\left({\mu }_{A_1}\left(x_1\right),{\nu }_{A_1}\left(x_1\right),{\pi }_{A_1}\left(x_1\right)\hspace{0.17em}\right)& \left({\mu }_{A_1}\left(x_2\right),{\nu }_{A_1}\left(x_2\right),{\pi }_{A_1}\left(x_2\right)\hspace{0.17em}\right)& \dots & \left({\mu }_{A_1}\left(x_n\right),{\nu }_{A_1}\left(x_n\right),{\pi }_{A_1}\left(x_n\right)\hspace{0.17em}\right)\\ \left({\mu }_{A_2}\left(x_1\right),{\nu }_{A_2}\left(x_1\right),{\pi }_{A_2}\left(x_1\right)\hspace{0.17em}\right)& \left({\mu }_{A_2}\left(x_2\right),{\nu }_{A_2}\left(x_2\right),{\pi }_{A_2}\left(x_2\right)\hspace{0.17em}\right)& \dots & \left({\mu }_{A_2}\left(x_n\right),{\nu }_{A_2}\left(x_n\right),{\pi }_{A_2}\left(x_n\right)\hspace{0.17em}\right)\\ \begin{array}{l}.\\ .\\ .\end{array}& \begin{array}{l}.\\ .\\ .\end{array}& \begin{array}{l}.\\ .\\ .\end{array}& \begin{array}{l}.\\ .\\ .\end{array}\\ \left({\mu }_{A_m}\left(x_1\right),{\nu }_{A_m}\left(x_1\right),{\pi }_{A_m}\left(x_1\right)\hspace{0.17em}\right)& \left({\mu }_{A_m}\left(x_2\right),{\nu }_{A_m}\left(x_2\right),{\pi }_{A_m}\left(x_2\right)\hspace{0.17em}\right)& \dots & \left({\mu }_{A_m}\left(x_n\right),{\nu }_{A_m}\left(x_n\right),{\pi }_{A_m}\left(x_n\right)\hspace{0.17em}\right)\end{array}\right]$$

(16)

Step 4. Construct an aggregated weighted intuitionistic fuzzy decision matrix for each criterion (C_i) and an alternative A_j using (Equation (4)) where W represents a set of grades of importance. It is obvious that the first term expresses a fuzzy intersection, and the second term expresses a fuzzy union.

Hence, the aggregated weighted intuitionistic fuzzy decision matrix can be defined as follows:

$$R^{’}=\left[\begin{array}{cccc}\left({\mu }_{A_{1}W}\left(x_1\right),{\nu }_{A_{1}W}\left(x_1\right),{\pi }_{A_{1}W}\left(x_1\right)\hspace{0.17em}\right)& \left({\mu }_{A_{1}W}\left(x_2\right),{\nu }_{A_{1}W}\left(x_2\right),{\pi }_{A_{1}W}\left(x_2\right)\hspace{0.17em}\right)& \dots & \left({\mu }_{A_{1}W}\left(x_n\right),{\nu }_{A_{1}W}\left(x_n\right),{\pi }_{A_{1}W}\left(x_n\right)\hspace{0.17em}\right)\\ \left({\mu }_{A_{2}W}\left(x_1\right),{\nu }_{A_{2}W}\left(x_1\right),{\pi }_{A_{2}W}\left(x_1\right)\hspace{0.17em}\right)& \left({\mu }_{A_{2}W}\left(x_2\right),{\nu }_{A_{2}W}\left(x_2\right),{\pi }_{A_{2}W}\left(x_2\right)\hspace{0.17em}\right)& \dots & \left({\mu }_{A_{2}W}\left(x_n\right),{\nu }_{A_{2}W}\left(x_n\right),{\pi }_{A_{2}W}\left(x_n\right)\hspace{0.17em}\right)\\ \begin{array}{l}.\\ .\\ .\end{array}& \begin{array}{l}.\\ .\\ .\end{array}& \begin{array}{l}.\\ .\\ .\end{array}& \begin{array}{l}.\\ .\\ .\end{array}\\ \left({\mu }_{A_{m}W}\left(x_1\right),{\nu }_{A_{m}W}\left(x_1\right),{\pi }_{A_{m}W}\left(x_1\right)\hspace{0.17em}\right)& \left({\mu }_{A_{m}W}\left(x_2\right),{\nu }_{A_{m}W}\left(x_2\right),{\pi }_{A_{m}W}\left(x_2\right)\hspace{0.17em}\right)& \dots & \left({\mu }_{A_{m}W}\left(x_n\right),{\nu }_{A_{m}W}\left(x_n\right),{\pi }_{A_{m}W}\left(x_n\right)\hspace{0.17em}\right)\end{array}\right]$$

(17)

Step 5. Determine the intuitionistic fuzzy positive ideal and intuitionistic fuzzy negative ideal solutions. And let them exist only with benefit criteria. A* is the intuitionistic fuzzy positive ideal solution and A—is the intuitionistic fuzzy negative ideal solution.

Then A* and A⁻ [44]:

$$\begin{array}{l}{A}^{*}=\left({\mu }_{A^{*}W}\left(x_j\right),\hspace{0.17em}{\nu }_{A^{*}W}\left(x_j\right)\right)\\ A^{-}=\left({\mu }_{A^{-}W}\left(x_j\right),\hspace{0.17em}{\nu }_{A^{-}W}\left(x_j\right)\right)\end{array}$$

(18)

where

$$\begin{array}{l}{\mu }_{A^{*}W}\left(x_j\right)\underset{}{\underset{i}{=\max }{\mu }_{AiW}\left(x_j\right)}\\ {\nu }_{A^{*}W}\left(x_j\right)\underset{}{\underset{i}{=\min }{\nu }_{AiW}\left(x_j\right)}\\ {\mu }_{A^{-}W}\left(x_j\right)\underset{}{\underset{i}{=\min }{\mu }_{AiW}\left(x_j\right)}\\ {\nu }_{A^{-}W}\left(x_j\right)\underset{}{\underset{i}{=\max }{\nu }_{AiW}\left(x_j\right)}\end{array}$$

(19)

Step 6. For each alternative, calculate the similarity from both the ideal and anti-ideal solutions. The similarity measures, i.e., the $S_{ij}^{\ast }$ and ${\mathrm{S}}_{ij}^{-}$ of each alternative from the intuitionistic fuzzy positive ideal and negative fuzzy ideal solutions, are calculated with respect to criterion C_j [32]:

$$\begin{gathered} {\mathrm{S}}_{ij}^{*}=1-\frac{\left|2\left({\mu }_{Aiw}\left(x_j\right)-{\mu }_{A^{\ast }w}\left(x_j\right)\right)-\left({\nu }_{Aiw}\left(x_j\right)-{\nu }_{A^{\ast }w}\left(x_j\right)\right)\right|}{3} \\ \hspace{1em}\hspace{1em}\ast \left(1-\frac{{\pi }_{Aiw}\left(x_j\right)+{\pi }_{A^{\ast }w}\left(x_j\right)}{2}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\frac{\left|2\left({\nu }_{Aiw}\left(x_j\right)-{\nu }_{A^{\ast }w}\left(x_j\right)\right)-\left({\mu }_{Aiw}\left(x_j\right)-{\mu }_{A^{\ast }w}\left(x_j\right)\right)\right|}{3} \\ \ast \frac{{\pi }_{Ai}w\left(x_j\right)+{\pi }_{A^{\ast }w}\left(x_j\right)}{2} \end{gathered}$$

(20)

$$\begin{gathered} {\mathrm{S}}_{ij}^{-}=1-\frac{\left|2\left({\mu }_{Aiw}\left(x_j\right)-{\mu }_{A^{-}w}\left(x_j\right)\right)-\left({\nu }_{Aiw}\left(x_j\right)-{\nu }_{A^{-}w}\left(x_j\right)\right)\right|}{3} \\ \hspace{1em}\hspace{1em}\ast \left(1-\frac{{\pi }_{Aiw}\left(x_j\right)+{\pi }_{A^{-}w}\left(x_j\right)}{2}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\frac{\left|2\left({\nu }_{Aiw}\left(x_j\right)-{\nu }_{A^{-}w}\left(x_j\right)\right)-\left({\mu }_{Aiw}\left(x_j\right)-{\mu }_{A^{-}w}\left(x_j\right)\right)\right|}{3} \\ \ast \frac{{\pi }_{Aiw}\left(x_j\right)+{\pi }_{A^{-}w}\left(x_j\right)}{2} \end{gathered}$$

(21)

Finally, a simple weighted model is used to assess the similarity measures over all criteria:

$$S_i^{\ast }=\sum _{j=1}^m{S}_{ij}^{\ast },S_i^{-}=\sum _{j=1}^m{S}_{ij}^{-}$$

(22)

Step 7. Calculate the relative closeness coefficient to the intuitionistic fuzzy ideal solution. The relative closeness coefficient of an alternative A_i with respect to the intuitionistic fuzzy ideal solution A* is defined as follows [36]:

$$C_{i^{\ast }}=\frac{S_i^{\ast }}{S_i^{\ast }+S_i^{-}} \mathrm{where} 0 \le C_{i^{\ast }}\le 1(\mathrm{i}=0,1,2,\dots .\mathrm{m})$$

(23)

Step 8. Rank the alternatives.

After the relative closeness coefficient is determined, alternatives are ranked according to the descending order of C_i*.

3. Results and Discussion

The applied method managed to gather valuable responses in a wide variety of questions posed in our attempt to address holistically the known issues related to the water management and measures planning in such a remote and heavily pressured river basin. The inclusiveness of stakeholders from all groups meant that their voices were heard and their opinions on the needs and problems were expressed, offering us the ability to order them hierarchically, assisting the decision makers. Furthermore, the objectivity and transparency of this method is a tool for conflict resolution.

Moving on to the actual findings that originated from the semi-structured interviews, the stakeholder group that is dependent on water, i.e., farmers, recognize the problem of river quantity and quality and are interested in finding solutions that will allow them to maintain their business operations.

The biggest concern for most stakeholders seem to be related to the quality of the water of the Laspias river, especially in drought periods. However, in the region of Dekarcho, the farmers also emphasize the water irrigation quantities. A significant percentage (≈78%) of the respondents believe that the Laspias river definitely needs some intervention, approximately 19% believe that some intervention may be necessary, while only one respondent (≈2.5%) believed that no intervention was necessary. Regarding groundwater, the corresponding percentages are ≈66% (27/41), ≈22% (9/41), and 5/41 (≈12%), respectively. The development of an irrigation network that will be based on the drilling of new municipal/public wells is advanced by the stakeholders (mainly farmers) as one of the best alternatives to deal with the water shortage in the area which is not affected by the Laspias River. It is also worth mentioned that approximately 53% of the respondents believe that irrigation can contribute to the economic development of the region in the future, while a significant percentage (≈34%) does not know what such an ecosystem service of the Laspias river could be.

Also of interest are the answers to the questions about what criteria farmers use to choose the type of crop they plant. The sample size in this question is n = 29 (crowd of farmers). According to the responses, economic efficiency is the most popular answer, followed by human productivity, defined as the ratio of the production divided by human work (in hours). Dryland or thirsty crops are not a selection criterion, except in the area around the settlement of Abdira, where most of the crops are dryland cotton due to the presence of the Abdira swell. Resistant crops, perennial, annual, or seasonal crops, and traditional crops are also not a selection criterion if the criteria of economic efficiency and lower employment are not met. Furthermore, the cultivators placed greater emphasis on the economic criterion, but also placed great importance on the environment (Figure 5).

As aforementioned, the following steps are used in order to achieve the multicriteria ranking under multiple stakeholders:

Step 1. Determine the weights of each participant. The importance of each participant was calculated with respect to the scale proposed by [37], that is, by considering the educational level and experience. Then, the weight of each participant can be obtained as a crisp value by using Equation (15) [41].

For instance, based on the answers, the first stakeholder was proficient (Pt), with μ = 0.5, v = 0.45, and π = 0.05, and therefore his weight:

$${\lambda }_{\kappa }=\frac{(0.5+0.05\ast \left(\frac{0.5}{0.5+0.45}\right))}{23.91053}=0.022$$

The denominator of this equation is estimated by summing all 43 numerators of the participants.

A total of 43 questionnaires was completed; of the total participants, 29 of them were farmers, and the rest were experts or administrative officers.

Step 2. Aggregate all information based on the participants by using the IFWA operator (Equation (14)). In this application, these steps concern mainly the weights of the criteria. As aforementioned, in this application, participants had different levels of practice and education, so the value λ takes different values. The final criteria’s weights, derived as fuzzy intuitionistic information, are presented in Table 1.

From the results, it is found that stakeholders put great importance on the environmental criterion and less on criteria involving various technical projects. However, the economical aspect seems as the most important criterion.

There might be some threads to validity for the faultless and reproducible methodology in acquiring stakeholders’ opinion, and for the methodology used for translating qualitative and quantitative information. However, the societal needs, values, and aspirations were expressed and could be integrated into planning. The findings could be dependent on prior training and knowledge but also reflect the participants’ social, political and cultural individual backgrounds. The stakeholder’s opinion might not be the most solid from a scientific point of view, but balancing of priorities and competing demands in an assimilable way by policy makers is exactly what is needed for operationalization of the basin.

Step 3. Construct an intuitionistic fuzzy decision matrix for each criterion (C_i) and alternative A_j by transforming the opinions of experts into Intuitionistic Fuzzy Values using (Equation (16)) (

Table 2. Intuitionistic fuzzy decision matrix (R).

R	C1			C2			C3			C4			C5			C6			C7			C8			C9			C10
	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π	μ	ν	π
A1	0.8	0.1	0.1	1	0	0	1	0	0	0.1	0.75	0.15	1	0	0	0.7	0.2	0.1	0.6	0.3	0.1	1	0	0	1	0	0	0.6	0.3	0.1
A2	0.8	0.1	0.1	0.8	0.1	0.1	0.4	0.5	0.1	0.5	0.4	0.1	0.4	0.5	0.1	0.8	0.1	0.1	0.6	0.3	0.1	0.25	0.6	0.15	0.5	0.4	0.1	0.6	0.3	0.1
A3	0.7	0.2	0.1	0.6	0.3	0.1	1	0	0	0.1	0.9	0	1	0	0	0.25	0.6	0.15	0.7	0.2	0.1	0.8	0.1	0.1	0.8	0.1	0.1	0.7	0.2	0.1
A4	0.1	0.9	0	1	0	0	0.7	0.2	0.1	1	0	0	0.8	0.1	0.1	1	0	0	1	0	0	0.4	0.5	0.1	0.8	0.1	0.1	1	0	0
A5	0.25	0.6	0.15	0.7	0.2	0.1	1	0	0	0.25	0.6	0.15	1	0	0	0.6	0.3	0.1	0.8	0.1	0.1	1	0	0	1	0	0	0.7	0.2	0.1
A6	0.4	0.5	0.1	0.8	0.1	0.1	0.8	0.1	0.1	0.4	0.5	0.1	0.5	0.4	0.1	0.7	0.2	0.1	0.5	0.4	0.1	0.8	0.1	0.1	0.8	0.1	0.1	0.6	0.3	0.1
A7	0.5	0.4	0.1	0.8	0.1	0.1	0.8	0.1	0.1	0.4	0.5	0.1	0.5	0.4	0.1	0.8	0.1	0.1	0.5	0.4	0.1	0.8	0.1	0.1	1	0	0	0.6	0.3	0.1
A8	0.7	0.2	0.1	0.7	0.2	0.1	0.1	0.75	0.15	0.1	0.9	0	0.1	0.9	0	0.8	0.1	0.1	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.7	0.2	0.1
A9	1	0	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0	0.1	0.9	0
A10	0.6	0.3	0.1	0.8	0.1	0.1	1	0	0	0.1	0.75	0.15	1	0	0	0.7	0.2	0.1	0.5	0.4	0.1	1	0	0	1	0	0	0.7	0.2	0.1
A11	0.7	0.2	0.1	1	0	0	1	0	0	0.1	0.75	0.15	0.7	0.2	0.1	1	0	0	0.6	0.3	0.1	0.5	0.4	0.1	1	0	0	0.6	0.3	0.1
A12	0.8	0.1	0.1	0.7	0.2	0.1	1	0	0	0.1	0.75	0.15	1	0	0	0.5	0.4	0.1	0.7	0.2	0.1	1	0	0	1	0	0	0.5	0.4	0.1
A13	0.8	0.1	0.1	0.8	0.1	0.1	1	0	0	0.1	0.75	0.15	1	0	0	0.8	0.1	0.1	0.7	0.2	0.1	0.6	0.3	0.1	1	0	0	0.8	0.1	0.1
A14	0.7	0.2	0.1	1	0	0	1	0	0	0.1	0.75	0.15	1	0	0	1	0	0	0.7	0.2	0.1	0.6	0.3	0.1	1	0	0	0.6	0.3	0.1

).

Step 4. Construct aggregated weighted intuitionistic fuzzy decision matrix for each criterion based on the alternative A_j and the corresponding weight using Equation (4).

Hence, the aggregated weighted intuitionistic fuzzy decision matrix is presented in

Table 3. Aggregated intuitionistic fuzzy decision matrix based on the opinions of decision makers (R′).

R’	C1			C2			C3			C4			C5			C6			C7			C8			C9			C10
	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π	μ ∗ w	ν + w − (v ∗ w)	π
A1	0.67	0.22	0.12	0.73	0.18	0.10	0.79	0.16	0.05	0.08	0.79	0.13	0.72	0.18	0.09	0.50	0.36	0.13	0.41	0.45	0.14	0.73	0.19	0.09	0.66	0.24	0.10	0.42	0.45	0.13
A2	0.67	0.22	0.12	0.58	0.26	0.16	0.32	0.58	0.10	0.39	0.50	0.12	0.29	0.59	0.12	0.58	0.28	0.14	0.41	0.45	0.14	0.18	0.67	0.14	0.33	0.54	0.13	0.42	0.45	0.13
A3	0.58	0.30	0.11	0.44	0.42	0.14	0.79	0.16	0.05	0.08	0.92	0.01	0.72	0.18	0.09	0.18	0.68	0.14	0.48	0.37	0.15	0.58	0.27	0.15	0.53	0.31	0.16	0.49	0.37	0.14
A4	0.08	0.91	0.00	0.73	0.18	0.10	0.55	0.33	0.12	0.77	0.16	0.07	0.58	0.26	0.16	0.72	0.20	0.08	0.69	0.21	0.10	0.29	0.59	0.12	0.53	0.31	0.16	0.70	0.22	0.09
A5	0.21	0.65	0.14	0.51	0.34	0.15	0.79	0.16	0.05	0.19	0.66	0.14	0.72	0.18	0.09	0.43	0.44	0.13	0.55	0.29	0.16	0.73	0.19	0.09	0.66	0.24	0.10	0.49	0.37	0.14
A6	0.33	0.57	0.10	0.58	0.26	0.16	0.63	0.24	0.12	0.31	0.58	0.11	0.36	0.51	0.13	0.50	0.36	0.13	0.34	0.53	0.13	0.58	0.27	0.15	0.53	0.31	0.16	0.42	0.45	0.13
A7	0.42	0.48	0.11	0.58	0.26	0.16	0.63	0.24	0.12	0.31	0.58	0.11	0.36	0.51	0.13	0.58	0.28	0.14	0.34	0.53	0.13	0.58	0.27	0.15	0.66	0.24	0.10	0.42	0.45	0.13
A8	0.58	0.30	0.11	0.51	0.34	0.15	0.08	0.79	0.13	0.08	0.92	0.01	0.07	0.92	0.01	0.58	0.28	0.14	0.07	0.92	0.01	0.07	0.92	0.01	0.07	0.92	0.01	0.49	0.37	0.14
A9	0.83	0.13	0.04	0.07	0.92	0.01	0.08	0.92	0.00	0.08	0.92	0.01	0.07	0.92	0.01	0.07	0.92	0.01	0.07	0.92	0.01	0.07	0.92	0.01	0.07	0.92	0.01	0.07	0.92	0.01
A10	0.50	0.39	0.11	0.58	0.26	0.16	0.79	0.16	0.05	0.08	0.79	0.13	0.72	0.18	0.09	0.50	0.36	0.13	0.34	0.53	0.13	0.73	0.19	0.09	0.66	0.24	0.10	0.49	0.37	0.14
A11	0.58	0.30	0.11	0.73	0.18	0.10	0.79	0.16	0.05	0.08	0.79	0.13	0.51	0.35	0.15	0.72	0.20	0.08	0.41	0.45	0.14	0.36	0.51	0.12	0.66	0.24	0.10	0.42	0.45	0.13
A12	0.67	0.22	0.12	0.51	0.34	0.15	0.79	0.16	0.05	0.08	0.79	0.13	0.72	0.18	0.09	0.36	0.52	0.12	0.48	0.37	0.15	0.73	0.19	0.09	0.66	0.24	0.10	0.35	0.53	0.12
A13	0.67	0.22	0.12	0.58	0.26	0.16	0.79	0.16	0.05	0.08	0.79	0.13	0.72	0.18	0.09	0.58	0.28	0.14	0.48	0.37	0.15	0.44	0.43	0.13	0.66	0.24	0.10	0.56	0.30	0.15
A14	0.58	0.30	0.11	0.73	0.18	0.10	0.79	0.16	0.05	0.08	0.79	0.13	0.72	0.18	0.09	0.72	0.20	0.08	0.48	0.37	0.15	0.44	0.43	0.13	0.66	0.24	0.10	0.42	0.45	0.13

using Equation (17).

Step 5. Determine intuitionistic fuzzy positive ideal (A*) and intuitionistic fuzzy negative ideal (A⁻) solutions. Let only the benefit criteria exist (

Table 4. Ideal and anti-ideal solutions expressed as intuitionistic fuzzy values with respect to criterion C_i.

	Ideal Solution			Anti-Ideal Solution
Criteria	μ	ν	π	μ	ν	π
1. Financial	0.8329	0.1303	0.0368	0.0833	0.9130	0.0037
2. Social	0.7280	0.1769	0.0951	0.0728	0.9177	0.0095
3. Environmental	0.7918	0.1591	0.0490	0.0792	0.9159	0.0049
4. Covering water needs	0.7706	0.1606	0.0688	0.0771	0.9161	0.0069
5. Resilience of measures to climate change	0.7245	0.1823	0.0932	0.0724	0.9182	0.0093
6. Local acceptance and expertise at prefecture level	0.7208	0.2033	0.0759	0.0721	0.9203	0.0076
7. Importance of the measure	0.6896	0.2122	0.0982	0.0690	0.9212	0.0098
8. Saving water	0.7297	0.1853	0.0850	0.0730	0.9185	0.0085
9. Synergy with other measures	0.6632	0.2376	0.0992	0.0663	0.9238	0.0099
10. Attracting new people to the countryside to live and work	0.6956	0.2174	0.0869	0.0696	0.9217	0.0087

).

Step 6. Calculate for each alternative the similarity from both the ideal and anti-ideal solutions.

The similarity measures, $S_i^{\ast }$ and $S_i^{-}$, for each alternative from the intuitionistic fuzzy positive ideal and intuitionistic fuzzy negative ideal solutions are calculated with respect to criterion C_i by using the Equations (18) and (19). Finally, a simple weighted model is used to assess the similarity measures over all criteria.

Step 7. Calculate the relative closeness coefficient to the intuitionistic fuzzy positive ideal solution.

The relative closeness coefficient of an alternative A_j with respect to the intuitionistic fuzzy ideal solution A* is defined as follows:

$$C_{i^{\ast }}=\frac{S_{i^{*}}}{S_{i^{*}}+S_{i^{-}}} \mathrm{where} 0 \le C_{i^{\ast }}\le 1(\mathrm{I}=0,1,2,\dots ,\mathrm{m})$$

Step 8. Rank the alternatives in descending order. The final results are presented in

Table 5. Final results using TOPSIS method with similarity measures based on IFWA weights.

Alternative	${\mathit{S}}_{\mathit{i}}^{\mathbf{*}}$	${\mathit{S}}_{\mathit{i}}^{-}$	Score (Ci)	Rank
Reuse of wastewater (A1)	8.473365	4.667272	0.6448	1
Inflow of Laspias river from a surplus water of the canals (A2)	7.001369	6.139268	0.5328	12
Changing crops to less water-intensive types (A3)	7.659083	5.481555	0.5829	10
Establishment of a centralized irrigation network (A4)	8.367324	4.773313	0.6368	4
Grant/use of automation in the irrigation activities (A5)	8.088582	5.052056	0.6155	7
Artificial recharge of groundwater utilizing excess water based on flood basin (A6)	7.449404	5.691233	0.5669	11
Artificial recharge of groundwater utilizing excess water based on ditch network (A7)	7.720442	5.420195	0.5875	9
Intensification of irrigation (A8)	5.226808	7.91383	0.3978	13
No change to the existing situation (A9)	3.901502	9.239136	0.2969	14
Redesign of production lines and internal recycling of water flows (A10)	8.182421	4.958217	0.6227	5
Removal/deactivation of pollutants (A11)	8.036232	5.104405	0.6116	8
Strict implementation of the pricing policy on water use (A12)	8.125107	5.01553	0.6183	6
Strict implementation of the pollution pricing policy (A13)	8.370581	4.770057	0.6370	3
Monitoring of system pollutants (A14)	8.382354	4.758283	0.6379	2

.

In addition, two main methods are examined. The first one is based on the concept of entropy (Appendix A). It differs from the proposed method since the concept of entropy is used instead of the IFWA operator in order to assess the weights of criteria. In this case, a main disadvantage is produced, which is that the questionnaires regarding the weight’s importance will not be considered. The method emphasized the criteria with low hesitancy; finally, the A₄ alternative is selected.

The second examined method is the method in [41]. The main difference between the proposed method and that one is that the Euclidean distance is used during the implementation of the TOPSIS method. The results are presented in

Table 6. Final results using TOPSIS method with Euclidean distances based on IFWA weights.

Alternative	${\mathit{S}}_{\mathit{i}}^{\mathbf{*}}$	${\mathit{S}}_{\mathit{i}}^{-}$	Score (Ci)	Rank
Reuse of wastewater (A1)	0.2516	0.5894	0.7008	1
Inflow of Laspias river from a surplus water of the canals (A2)	0.3274	0.4412	0.5740	12
Changing crops to less water-intensive types (A3)	0.3183	0.5229	0.6216	11
Establishment of a centralized irrigation network (A4)	0.2900	0.5846	0.6684	6
Grant/use of automation in the irrigation activities (A5)	0.2816	0.5532	0.6627	7
Artificial recharge of groundwater utilizing excess water based on spreading basin (A6)	0.2856	0.4772	0.6256	10
Artificial recharge of groundwater utilizing excess water based on ditch network (A7)	0.2662	0.5031	0.6540	9
Intensification of irrigation (A8)	0.5443	0.3447	0.3877	13
No change to the existing situation (A9)	0.6571	0.2425	0.2695	14
Redesign of production lines and internal recycling of water flows (A10)	0.2704	0.5622	0.6752	4
Removal/deactivation of pollutants (A11)	0.2798	0.5487	0.6623	8
Strict implementation of the pricing policy on water use (A12)	0.2761	0.5598	0.6697	5
Strict implementation of the pollution pricing policy (A13)	0.2483	0.5781	0.6996	2
Monitoring of system pollutants (A14)	0.2580	0.5796	0.6919	3

.

Regarding the two TOPSIS methods, they have little deviation in the results; however, the results based on the similarity measure are slightly preferred due to the fact that this measure leads to more balanced (centripetal) solutions, and, furthermore, it overcomes drawbacks, such as the “the division by zero problem”. Hence, the reuse of wastewater (A₁), strict implementation of the pollution pricing policy (A₁₃), and the monitoring of system pollutants (A₁₄) are selected most often. In addition, by using the widely used TOPSIS, the alternative A₄ has a lower rank.

The main difference is that the similarity-based TOPSIS puts emphasis on the alternative of creating a central irrigation network (fourth choice). In fact, this choice restores the water regime situation before the great river infrastructure. It is very encouraging that the alternative of doing nothing is last in preference among all the methods. It should be noted that these three first alternatives (strict implementation of the pollution pricing policy (A₁₃), monitoring of system pollutants (A₁₄), and wastewater reuse (A₁) can be characterized as eco-friendly. The final ranking could be characterized rather as rational and balanced. Therefore, the similarity measures that are used have a theoretical sound foundation and lead to balanced solutions. Therefore, this research provides a series of acceptable measures that lead to the hierarchy of problems as were recognized by the stakeholders.

Consequently, the use of the IFWA operator to combine the aspects of the weight and the intuitionistic fuzzy similarity-based TOPSIS method is selected because of its balanced outcomes. The benefits of this method, i.e., transparency and objectivity, can assist WFD application in the RBMPs program of measures consultation. In particular, given the delay in decision making and mitigation measures planning, it can assist the actual dual nature of WFD (humans and the environment) by providing the means to determine hierarchy, given the cost, time, and water scarcity/deficiency.

It is worth mentioning that, regarding the alternative A₄ (which is ranked first when the entropy method is applied), a previous study [45], has substantiated that it is possible to transfer water from the Nestos river and create a large and organized irrigation network that will meet the water needs of the wider area and simultaneously have environmental benefits. According to the same study, the annual volume of the Nestos river is approximately estimated at 788 × 10⁶ m³, exceeding the beneficial volume of the main (from a reservoir system) reservoir of Thesauros, which is 570 × 10⁶ m³. It should be pointed out that only 3000 ha of the land located between the Nestos river and the Laspias river are irrigated by the water of the Nestos river, 16,000 ha in the prefecture of Kavala, to the west of Nestos river, are irrigated by that river. Irrigation of the hectares of the area under consideration is mainly carried out with a system of open canals. Thus, in a way, the natural recharge of the aquifers, which was contributed to by the Nestos Delta, has been artificially compensated for since 1955, when the Nestos river was regulated and many structures were built.

4. Conclusions

The methodological approach designed for this study, based on the principles of participatory approach and intuitionistic fuzzy approach, have proven to be useful for addressing complex problems related to water quality, quantity, and uses while setting the hierarchy for catchment operationalization concerning the measures’ planning. During the process of this study, the scientific team managed to empower local people, including traditionally disadvantaged groups, especially in such a remote area. This ultimately created greater effectiveness in suggestions that were more participatory for operationalized water management. The mathematical “enablers” achieved were able to encompass a multi-stakeholder collaboration and create an operational model applicable for all river basins.

This work presents a multicriteria group decision making model to rank several water resource measures against the water crisis using intuitionistic fuzzy TOPSIS and emphasizing the integration of local experience and knowledge. The use of the intuitionistic fuzzy sets is a suitable way to deal with uncertainty, especially in cases that include qualitative information. This fact enables us to incorporate group decision making methodologies during the decision phase. Hence, the IFWA (intuitionistic fuzzy weighted averaging) operator was implemented to aggregate opinions of decision makers. The intuitionistic fuzzy TOPSIS method is used by choosing suitable similarity measures. Hence, a complicated solution can be modulated that consists of the reuse of wastewater (A₁), strict implementation of the pollution pricing policy (A₁₃), monitoring of system pollutants (A₁₄), and the creation of a central irrigation network or the modernization of the existing one (A₄). The methodology was compared with the intuitionistic TOPSIS based on the Euclidean distance measure [41]. Furthermore, the methodology was applied using weights derived by the entropy measures.

An interesting point is that, according to Greek conditions, there are a variety of basins and hydrological regimes, and, hence, the results cannot be generalized or duplicated in all basins as the ranking of the alternatives could be different. However, the proposed methodology is actually a tool that can make sure that all voices are heard as well as an objective method that can surpass conflicts through a common “technical” language that has multiple applications for planning depending on the questions posed, thereby assisting in strategic water resources management.