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Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 12081

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Special Issue Editors

Prof. Dr. Svajonė Bekešienė

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Guest Editor

Research Group on Logistics and Defence Technology Management, Lithuanian Military Academy, Silo 5a, 10322 Vilnius, Lithuania
Interests: multi-purpose decision-making tasks; mathematical modeling; advances in theoretical mathematics and statistics (structural equation modeling); fuzzy logic; risk assessment and management
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Ieva Meidutė-Kavaliauskienė

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Guest Editor

1. Research Group on Logistics and Defense Technology Management, General Jonas Žemaitis Military Academy of Lithuania, Šilo st. 5A, LT-10322 Vilnius, Lithuania
2. Business Management, Vilnius Gediminas Technical University (VILNIUS TECH), Sauletekio al. 11, LT-10233 Vilnius, Lithuania
Interests: logistics; supply chain management; modelling; integrating processes; 3 PL
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Risk management is a decision-making process that takes into consideration political, social, economic and engineering factors, with relevant risk assessments relating to a potential hazard. Mathematics uses reasoned theories, computational techniques, algorithms, and the latest computer technologies to solve the problems arising from various fields, such as economics, engineering, business and social sciences. Mathematics also focuses on problems coming from the industry, and creates solutions relevant to the industry, including finding the most efficient and cost-effective way to solve these problems. It allows the development, analysis and comparison of regulatory options, as well as the selection of the optimal regulatory response for safety from that hazard.

Reliability engineering and risk management have been attracting increasing amounts of attention, and are of growing importance in civil, mechanical, aerospace and aeronautics, offshore and marine engineering, as well as in many other disciplines of engineering. Against this background, the aim of this Special Issue is to bring scientists all over the world together to present their research on innovative methodologies, and the practical applications of these technologies in the field of reliability engineering and risk management. Emerging concepts, as well as the state of the art and novel applications of reliability principles and risk-based decision-making in all types of structures, infrastructures and mechanical systems, will be emphasized within the scope of the issue. In this context, articles on theories, methods, algorithms and applications are all welcome.

This special issue focuses on the characterization of uncertainties and the development of risk assessment models for the essential infrastructures in different areas of life. Both practical applications for reliability-based design code calibration and quantitative risk assessment, and novel methodological developments, including emerging areas, such as machine learning and artificial intelligence, are included to provide a reliable method for multifaceted risk assessment. We invite you to contribute and submit your latest research work.

Prof. Dr. Svajonė Bekešienė
Prof. Dr. Ieva Meidute-Kavaliauskiene
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Bayesian methods
Damage analysis and assessment
Decision analysis
Nonlinear models
Stochastic dynamics and controls
Structural health monitoring
Risk assessment models
Socioeconomic aspects of resilience and sustainability
Maintenance strategy based on risk cost optimization

Published Papers (7 papers)

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Research

21 pages, 1814 KiB

Open AccessArticle

Mathematical–Statistical Nonlinear Model of Zincing Process and Strategy for Determining the Optimal Process Conditions

by Alena Vagaská

Mathematics 2023, 11(3), 771; https://0-doi-org.brum.beds.ac.uk/10.3390/math11030771 - 03 Feb 2023

Cited by 2 | Viewed by 1060

Abstract

The article is aimed at the mathematical and optimization modeling of technological processes of surface treatments, specifically the zincing process. In surface engineering, it is necessary to eliminate the risk that the resulting product quality will not be in line with the reliability requirements or needs of customers. To date, a number of research studies deal with the applications of mathematical modeling and optimization methods to control technological processes and eliminate uncertainties in the technological response variables. The situation is somewhat different with the acid zinc plating process, and we perceive their lack more. This article reacts to the specific requirements from practice for the prescribed thickness and quality of the zinc layer deposited in the acid electrolyte, which stimulated our interest in creating a statistical nonlinear model predicting the thickness of the resulting zinc coating (ZC). The determination of optimal process conditions for acid galvanizing is a complex problem; therefore, we propose an effective solving strategy based on the (i) experiment performed by using the design of experiments (DOE) approach; (ii) exploratory and confirmatory statistical analysis of experimentally obtained data; (iii) nonlinear regression model development; (iv) implementation of nonlinear programming (NLP) methods by the usage of MATLAB toolboxes. The main goal is achieved—regression model for eight input variables, including their interactions, is developed (the coefficient of determination reaches the value of R² = 0.959403); the optimal values of the factors acting during the zincing process to achieve the maximum thickness of the resulting protective zinc layer (the achieved optimum value t_h* = 12.7036 μm), are determined. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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9 pages, 266 KiB

Open AccessArticle

Linear Diophantine Fuzzy Subspaces of a Vector Space

by Madeleine Al-Tahan, Sarka Hoskova-Mayerova, Saba Al-Kaseasbeh and Suha Ali Tahhan

Mathematics 2023, 11(3), 503; https://0-doi-org.brum.beds.ac.uk/10.3390/math11030503 - 17 Jan 2023

Cited by 2 | Viewed by 953

Abstract

The notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applicable to model vagueness in many real-life problems. On the other hand, subspaces of vector spaces are of great importance in many fields of science. The aim of this paper is to combine the two notions. In this regard, we consider the linear diophantine fuzzification of a vector space by introducing and studying the linear diophantine fuzzy subspaces of a vector space. First, we studied the behaviors of linear diophantine fuzzy subspaces of a vector space under a linear diophantine fuzzy set. Second, and by means of the level sets, we found a relationship between the linear diophantine fuzzy subspaces of a vector space and the subspaces of a vector space. Finally, we discuss the linear diophantine fuzzy subspaces of a quotient vector space. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

11 pages, 643 KiB

Open AccessArticle

Validating Measurement Structure of Checklist for Evaluating Ergonomics Risks in Heavy Mobile Machinery Cabs

by Vesna Spasojević Brkić, Mirjana Misita, Martina Perišić, Aleksandar Brkić and Zorica Veljković

Mathematics 2023, 11(1), 23; https://0-doi-org.brum.beds.ac.uk/10.3390/math11010023 - 21 Dec 2022

Viewed by 1600

Abstract

Heavy mobile machinery cabs and their equipment are still not well adjusted to operators, so it is not surprising that we are still witnessing huge consequences of accidents at sites where they operate. The checklist with 39 questions, based on the previous research, is formed, and its’ measurement structure has been tested on the sample of 102 transport, construction, and mining machines, including cranes, excavators, bucket wheel excavators, bulldozers, loaders, graders, backhoe loaders, trenchers, dump trucks, and scrapers by correlation analysis, Cronbach’s alpha, Spearman-Brown and Kendall’s W coefficient, exploratory factor analysis, and confirmatory factor analysis. The results validate the measurement structure of a checklist with only 17 items and five constructs. The results show that special attention should be put to the design of armrests and working conditions/exhaust gases, which are negatively correlated to cab interior space and task visibility. All other correlations between seat characteristics, the characteristics of armrests, whole-body vibration influences, reaching commands, the characteristics of cab interior space and environments, and interpersonal relationships are positive, which means that improvements to one area lead to improvements in another. Accordingly, the proposed model should be used for the fast, efficient, and cost-effective evaluation of ergonomics risks and as a guideline for further cab design improvements. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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25 pages, 4085 KiB

Open AccessArticle

Mathematical Modeling and Nonlinear Optimization in Determining the Minimum Risk of Legalization of Income from Criminal Activities in the Context of EU Member Countries

by Alena Vagaská, Miroslav Gombár and Antonín Korauš

Mathematics 2022, 10(24), 4681; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244681 - 09 Dec 2022

Cited by 2 | Viewed by 1335

Abstract

Legalization of the proceeds of crime represents a worldwide problem with serious economic and social consequences. Information technologies in conjunction with advanced computer techniques are important tools in the fight against money laundering (ML), financial crime (FC) and terrorism financing (TF). Nowadays, the applied literature on ML/FC/TF uses much more mathematical modelling as a solving strategy to estimate illicit money flows. However, we perceive that there is preference of linear models of economical dependences and sometimes lack of acceptance of nonlinearity of such investigated economic systems. To characterize the risk of legalization of crime proceeds in a certain country, the scientific researchers use the Basel anti-money laundering (AML) index. To better understand how the global indicators (WCI, CPI, EFI, GII, SEDA, DBI, GSCI, HDI, VAT_GAP, GDP per capita) affect the level of risk of ML/TF in the countries of EU, the authors use a unique data set of 24 destination countries of EU over the period 2012–2019. The article deals with two main research goals: to develop a nonlinear model and optimize the ML/TF risk by implementation of nonlinear optimization methods. The authors contribute: (i) providing the cross-country statistical analysis; (ii) creating the new nonlinear mathematical-statistical computational model (MSCM); and (iii) describing the observed dependent variable (Basel AML index). This study deepens previous knowledge in this research field and, in addition to the panel regression analysis, also applies nonlinear regression analysis to model the behavior of the investigated system (with nonlinearity). Our results point out the differences between the estimates of the investigated system behavior when using panel and nonlinear regression analysis. Based on the developed MSC model, the optimization procedure is conducted by applying an interior point method and MATLAB toolboxes and the second goal is achieved: the statement that such values of input variables at which the risk of legalization of income from criminal activity will be minimal. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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23 pages, 3958 KiB

Open AccessFeature PaperArticle

Mathematical Modelling of Qualitative System Development

by Jan Lánský, Jiří Mihola and Petr Wawrosz

Mathematics 2022, 10(15), 2752; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152752 - 03 Aug 2022

Cited by 1 | Viewed by 1259

Abstract

Many scientific fields need to know how human systems develop. From an economic point of view, the main factors of system output change are changes in the quantity of inputs (extensive factors) and changes in efficiency (input quality and productivity, intensive factors). The growth accounting (GA) method is used for the calculation of the impact of both factors on GDP change. However, its interpretation is sometimes difficult, and GA does not cover all of the possible situations of system (country economy) development. This article uses mathematical tools to derive new indicators (dynamic intensity indicator and dynamic extensity indicator) that clearly count and express how the changes in intensive or extensive factors contribute to the output change in any system. The indicators come from the complex system development typology analyzed in the text. The typology covers all of the relationships among the inputs, their efficiency, and their output. The article shows the use of these indicators in macroeconomics when examining the intensity of GDP development in the World’s major economies during the period of 1961–2021 and in microeconomics while investigating the intensity of the development Apple in the period of 1999–2021. We further discuss how indicators reduce managerial risk and uncertainty and their pros and cons. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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24 pages, 16475 KiB

Open AccessArticle

The Complex Systems for Conflict Interaction Modelling to Describe a Non-Trivial Epidemiological Situation

by Svajone Bekesiene, Igor Samoilenko, Anatolij Nikitin and Ieva Meidute-Kavaliauskiene

Mathematics 2022, 10(4), 537; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040537 - 09 Feb 2022

Cited by 4 | Viewed by 1373

Abstract

This study investigates a complex system that describes a non-trivial epidemiological model with integrated internal conflict (interregional migration) on the example of cyclic migration using the software. JetBrains PyCharm Community Edition 2020.3.3, a free and open-source integrated development environment (IDE) in the Python programming language, was chosen as the software development tool. The Matplotlib 3.5 library was used to display the modelling results graphically. The integration of internal conflict into the model revealed significant and notable changes in its behavior. This study’s results prove that not only the characteristics of the interaction factors but also the size of the values determine the direction of migration concerning relation to competitors. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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16 pages, 864 KiB

Open AccessArticle

A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

by Dragiša Stanujkić, Darjan Karabašević, Gabrijela Popović, Predrag S. Stanimirović, Muzafer Saračević, Florentin Smarandache, Vasilios N. Katsikis and Alptekin Ulutaş

Mathematics 2021, 9(13), 1554; https://0-doi-org.brum.beds.ac.uk/10.3390/math9131554 - 01 Jul 2021

Cited by 17 | Viewed by 3014

Abstract

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn. Full article

(This article belongs to the Special Issue Mathematical Modelling and Hybrid Strategies for Risk and Uncertainty Management)

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