Special Issue "Multiple Criteria Decision Making"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 November 2020.

Special Issue Editors

Assoc. Prof. Dr. Violeta Kersuliene
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Guest Editor
Department of Law, Business Management faculty, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania
Interests: operations research; optimization and decision analysis; multicriteria decision making; MCDM; multiple-criteria optimization; multiattribute decision making (MADM); multiobjective optimization (MODM); approximations; mathematics for decision making; decision support systems; evaluation sustainable development; civil engineering; management; knowledge management; game theory and economical computing; finance engineering; algorithms and software engineering; energy; fuzzy set theory; negotiations; the consensus in groups
Prof. Dr. Zenonas Turskis
Website1 Website2
Guest Editor
Laboratory of Operations Research, Institute of Sustainable Construction, Faculty of Civil Engineering, Vilnius Gediminas Technical University LT-10223 Vilnius, Saulėtekio al. 11, Lithuania.
Interests: operations research; optimization and decision analysis; multicriteria decision making; MCDM; multiple-criteria optimization; multiattribute decision making (MADM); multiobjective optimization (MODM); approximations; mathematics for decision making; decision support systems; evaluation sustainable development; civil engineering; management; knowledge management; game theory and economical computing; finance engineering; algorithms and software engineering; energy; fuzzy set theory; negotiations; the consensus in groups
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Special Issue Information

Dear Colleagues,

Decision making is one of the most critical topics in various areas of human activity and shows how to make 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 as a decision-making process to get the most out of available resources for the best attainable 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 as 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 requires the use of analytical methods that examine trade-offs, consider multiple scientific, political, economic, ecological and social dimensions, and reduces 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 that include but are not limited to business management, logistics, supply chains, energy, urban development, waste management, and others. In decision-making theories as well as 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, the 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 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.

Hence, 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 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 concerned 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 industries are invited to submit papers that explore aspects of multiobjective or multiattribute modeling and optimization in a crisp or uncertain environment and will elaborate on the state-of-the-art case studies in selected areas of application related to sustainable development decision aiding. 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, on the one hand, new mathematical tools and, on the other, economics and finance issues.

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 allows capturing uncertainty, imprecision, inaccurate definition of a decision problem and, as a consequence, fuzzing the issue.

As editors, we invite original research papers in this Special Issue that report on 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 is 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 the MCDM and related fields. It is undoubtedly 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 the 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 multi-objective 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 problem
  • 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.

Assoc Prof. Dr. Violeta Kersuliene
Prof. Dr. Zenonas Turskis
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 papers will be 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 monthly 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 1200 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.


  • Application of MCDM methods
  • Application of the interactive MCDM methods
  • Application of uncertainty MCDM approaches
  • Applications of fuzzy MCDM methods
  • Applications of outranking MCDM methods
  • Conditional value-at-risk
  • Conflict resolution
  • Data mining tools
  • Decision making
  • Fuzzy (uncertain, imprecise, ill-determined) decision problems
  • Fuzzy reasoning
  • Fuzzy sets
  • Grey systems
  • Group decision making
  • Hybrid decision-making analysis
  • Information technologies in decision making
  • Innovative applications of MCDM methods
  • Interval-valued fuzzy sets
  • Intuitionistic fuzzy sets
  • Lexicographic approach
  • Life-cycle analysis
  • mathematical programming in MCDM
  • MCDM in strategic management
  • Multicriteria decision aid
  • Multicriteria decision making
  • Multidimensional measurement framework
  • Multiobjective decision making
  • Multiple-criteria analysis
  • Multiple-criteria decision making
  • MCDM in Negotiations
  • Neutrosophic decision-making theories and methods
  • New trends in multicriteria evaluation
  • Optimization
  • Optimization techniques
  • Ordinal proximity measures
  • Outranking MCDM methods
  • Pareto frontier
  • Portfolio optimization
  • Procurement
  • Reference point method
  • Rough set theory
  • Variational analysis
  • Weighting approach

Published Papers (1 paper)

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Open AccessArticle
A Revised Inverse Data Envelopment Analysis Model Based on Radial Models
Mathematics 2020, 8(5), 803; https://doi.org/10.3390/math8050803 - 15 May 2020
In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be [...] Read more.
In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be unreliable as they neglect slacks while evaluating decision-making units’ (DMUs) overall efficiency level, whereas classic radial DEA models measure the efficiency level through not only radial efficiency index but also slacks. This paper points out these disadvantages with a counterexample, where current inverse DEA models give results that outputs shall increase when inputs decrease. We show that these unreasonable results are the consequence of existing inverse DEA models’ failure in preserving DMU’s efficiency level. To rectify this problem, we propose a revised model for the situation where the investigated DMU has no slacks. Compared to existing radial inverse DEA models, our revised model can preserve radial efficiency index as well as eliminating all slacks, thus fulfilling the requirement of efficiency level invariant. Numerical examples are provided to illustrate the validity and limitations of the revised model. Full article
(This article belongs to the Special Issue Multiple Criteria Decision Making)
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