Dear Colleagues,

Decision making is one of the most critical topics in various areas of human activity, and the field involves  making the right decisions to reach the end goal. Decision makers over the past few decades have successfully used multicriteria decision-making (MCDM) approaches to solve complex decision-making problems in a variety of fields, such as economics, finance, logistics, environmental remediation, business, engineering, medicine, law, and more. Decision makers need MCDM tools that help to balance conflicting goals with multiple choices and limited resources and time for decision makers to match conflicting goals.

Therefore, the use of the MCDM methods for solving problems in different fields is prevalent and helps in making significant decisions. MCDM is an effective systematic and quantitative way to deal with issues in the presence of several alternatives and several usually different criteria. Decision making regarding very complex problems, including business-related decisions and real-life decisions, requires an appropriate and reliable decision-support system. Optimization may be considered a decision-making process to get the most out of available resources to obtain the best possible results. Many real-world problems are multifaceted or multiattribute problems, which naturally involve multiple competing goals that need to be optimized at the same time within certain constraints or by choosing from the available discrete alternatives. In contrast to single-goal optimization, solutions to multiobjective and multiattribute problems correspond to a set of solutions with trade-offs, each expressing a peculiar trade-off between different goals or attributes. Optimization can be considered a decision-making process to maximize the effectiveness of the available resources used to achieve the best results possible.

 Considering, planning, and appropriate decision making require the use of analytical methods that examine trade-offs, consider multiple scientific, political, economic, ecological and social dimensions, and reduce possible conflicts in an optimizing framework. MCDM techniques fall into two major groups. The first group is discrete MCDM, including multiattribute utility theory (MAUT), analytic hierarchy process/analytic network process (AHP/ANP), and outranking methods, where the decision maker has to evaluate a finite set of alternatives to a) select the best option, b) rank alternatives from the best to worst, and c) classify alternatives into predefined classes or the described options (i.e., multiattribute decision-making (MADM) methods). The second is continuous MCDM, including multiobjective programming and goal programming, where there is an infinite set of alternatives (i.e., multiobjective decision-making (MODM) methods).

MCDM approaches are considered the established methods to aid decision makers in taking suitable decisions, and their applications are growing in popularity in many fields, including but are not limited to business management, logistics, supply chains, energy, urban development, waste management, and others. In decision-making theories and in business practice, decision makers encounter many imprecise concepts. Imprecise data are the premises which serve the specification of economic models and, consequently, the decision-making process. All this requires the utilization of the vague interference rule. In the second half of the 20th century, we witnessed the development of the behavioral economy. The world of economic concepts and models became even more imprecise. In addition, design, planning, and operations management rely on mathematical models, the complexity of which depends on the detail of models and complexity/characteristics of the problem they represent. It is thus no surprise that with the ever-increasing complexity of the issues, optimization comes with an inherent facet of uncertainty conveyed in different formal ways and calls for innovative approaches to produce optimal and interpretable solutions. Today’s real-world problems involve multiple data sets, some precise or objective and some uncertain or subjective. Many decision problems manage linguistic information assessed through several ordered qualitative scales. In these contexts, the main question arising is how to aggregate this qualitative information. This Special Issue welcomes MCDM procedures that rank a set of alternatives assessed using a specific non-uniform ordered qualitative scale for each criterion. Therefore, ordinal models to manage the ordinal degree of proximity from different ordered qualitative sizes are essential to this issue. Moreover, decision makers often make decisions in the face of the unknown.

A wide range of statistical and nonstatistical decision-making techniques have been proposed in the literature to model complex business processes. Unfortunately, decision making by humans is often suboptimal in ways that can be reliably predicted. Fuzzy set theory laid the foundations for significant modeling uncertainty, vagueness, and imprecision. The method of fuzzy sets noted substantial progress in economics in both theoretical and practical studies. MCDM has considerably expanded beyond classical and formal methodologies and has also involved intuitive and informal processes. Therefore, in addition to conventional MCDM methods, this Special Issue also welcomes their integration with uncertainty theory, such as fuzzy sets, rough sets, neutrosophic sets, etc.

Different mathematical models of real-life multicriteria optimization problems can be applied to various uncertain frameworks, with particular emphasis on real-life optimization problems. Neutrosophic logic, set, probability, statistics, and others are respectively generalizations of fuzzy and intuitionistic fuzzy logic and set, classical and imprecise probability, classical statistics, and others. Furthermore, the process industry seeks not only to minimize cost but also to minimize adverse environmental and social impacts. On the other hand, to give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex, and a wide range of optimization techniques and methodologies are used to minimize risks or improve quality in making concomitant decisions. The importance of strategic behavior in the human and social world is increasingly recognized in theory and practice. As a result, multicriteria optimization models and applications have emerged as a fundamental tool in pure and applied research. Multicriteria optimization models and applications strongly support decision-making processes in an interactive environment. They draw on mathematics, economics, statistics, engineering, biology, political science, operations research, and other subjects. A multioptimization occurs when multiple criteria considered by a decision maker are evaluated with mathematical optimization problems involving more than one objective function to be optimized simultaneously. The decision maker finds a set of objectives in a situation in which each goal is possibly conflicting, possibly equally important, or perhaps overlapping. The problem is then to determine the trade-off between objectives to support the decision-making process. Additionally, a sensitivity analysis should be done to validate/analyze the influence of uncertainty regarding decision making.

In this Special Issue, researchers from academia and industry are invited to submit papers that explore aspects of multiobjective or multiattribute modeling and optimization in a crisp or uncertain environment. The Issue will elaborate on the state-of-the-art case studies in selected areas of application related to sustainable development decision support. Analytical models, empirical studies, and case-based studies are all welcome, as long as the research work provides new insights and implications for the practice of decision making.

In recent years, new mathematical developments have been applied in the context of financial economics. Thus, a relevant challenge is to provide a bridge between new mathematical tools on the one hand and economics and finance issues on the other.

Articles are welcome on this issue where systemic solutions in practical decision making that bring economic, social, and environmental benefits are offered through a variety of methodologies and tools (e.g., information technologies and multiple-criteria decision-making methods). Articles that propose new methods dealing with multifaceted issues are also welcome.

Since the pioneering paper of Zadeh, many extensions of the fuzzy set theory with practical applications in different areas have also been proposed, including intuitionistic fuzzy sets, interval-valued fuzzy sets, interval-valued intuitionistic fuzzy sets, rough sets, bipolar fuzzy sets, grey sets, hesitant fuzzy sets, fuzzy numbers, and fuzzy oriented sets, among others. The multivalued logic and the lattice are the theoretical background of fuzzy set theory. MCDM methods for handling imprecision and vagueness in real decision-making problems are used in several different areas. The fuzzy set theory makes it possible to capture uncertainty, imprecision, inaccurate definitions of decision problems and, as a consequence, fuzzing the issue.

As Guest Editors, we invite original research papers for this Special Issue that report on the state-of-the-art and recent advancements in multicriteria decision making using the fuzzy or vague determined environment to computing, group decision-making problems, pattern recognition, information processing, and many other practical achievements.

The objective of this Special Issue is to gather a collection of papers reflecting the latest developments in practical applications of the MCDM mathematical tools and the latest developments in the mathematical programming methods of operations research for multicriteria optimization for different fields of multicriteria optimization approaches, models, applications and techniques. The use of some factor models to manage potential risks and other applications in economic theory and modeling are also of interest.

The scope of this Issue covers MCDM in a broad sense, focusing on recent advances in both discrete and continuous techniques and significant applications in different fields.

This Special Issue focuses on the science and art of multicriteria decisions, especially in multidisciplinary settings. We expect to publish high-quality papers in the categories of discovery, integration, application, and teaching of multicriteria decisions.

We invite authors to submit original research and review articles which give a more in-depth insight into the applications of MCDM theories in real-life problem-solving.

We hope that this Special Issue will stimulate both theoretical and applied research on MCDM and related fields. It is impossible in this short editorial to provide a more comprehensive description of all potential articles in this Special Issue.

We invite authors to submit original research articles which propose novel MCDM optimization models for solving real-life-related problems.

• Decent work and economic growth.
• Industry, innovation, and infrastructure.
• Sustainable development.
• Responsible resource consumption and production.
• Climate action.
• Peace, justice and strong institutions.

The proposed papers should present advanced MCDM systems related to the following directions of quantified decision making:

• Applications of MCDM.
• Modeling of MCDM.
• Decision analysis for sustainable production and consumption.
• Decision support systems.
• Discrete and continuous MCDM.
• Economic diagnosis and forecasting.
• Fuzziness in MCDM.
• Granular computing-based multiobjective or multiattribute optimization.
• Group decision making.
• Integrated approaches for modeling decision making.
• Intuitiveness in MCDM.
• MCDM methodologies.
• MCDM theories.
• MCDM in strategic management.
• MCDM design issues.
• Multigoal decisions.
• MODM intelligence problem.
• Multistage multiobjective or multiattribute problems.
• MCDM negotiation and group decisions.
• Neural-network-based multiobjective or multiattribute optimization.
• Risk management.
• Soft-computing techniques for MCDM.
• Survey and theoretical articles, as well as application papers.
• The development of MCDM Methods capable of capturing sustainability.
• The development of MCDM methods capable of capturing sustainability and fuzziness (uncertainty, imprecision and inaccurate definition) of the decision problem.
• Tools for multicriteria decisions.

We are motivated by the overriding aim to indicate the connections between MCDM systems and real-life problems.

Dr. Violeta Kersuliene
Prof. Dr. Zenonas Turskis
Guest Editors

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• Decent work and economic growth
• Industry, innovation, and infrastructure
• Sustainable development
• Responsible resource consumption and production
• Climate action
• Applications of MCDM
• Modeling of MCDM
• Decision analysis for sustainable production and consumption
• Decision support systems
• Discrete and continuous MCDM
• Economic diagnosis and forecasting
• Fuzziness in MCDM
• Granular computing-based multiobjective or multiattribute optimization
• Group decision making
• Integrated approaches for modeling decision making
• Intuitiveness in MCDM
• MCDM methodologies
• MCDM theories
• MCDM in strategic management
• MCDM design issues
• Multigoal decisions
• MODM intelligence problem
• Multistage multiobjective or multiattribute problems
• MCDM negotiation and group decisions
• Neural-network-based multiobjective or multiattribute optimization
• Risk management
• Soft-computing techniques for MCDM
• Survey and theoretical articles, as well as application papers
• The development of MCDM Methods capable of capturing sustainability
• The development of MCDM methods capable of capturing sustainability and fuzziness (uncertainty, imprecision and inaccurate definition) of the decision problem
• Tools for multicriteria decisions