Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) methods. To achieve that, a set of feasible MCDA methods was identified. Based on reference literature guidelines, a simulation experiment was planned. The formal foundations of the authors’ approach provide a reference set of MCDA methods ( Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Complex Proportional Assessment (COPRAS), and PROMETHEE II: Preference Ranking Organization Method for Enrichment of Evaluations) along with their similarity coefficients (Spearman correlation coefficients and WS coefficient). This allowed the generation of a set of models differentiated by the number of attributes and decision variants, as well as similarity research for the obtained rankings sets. As the authors aim to build a complex benchmarking model, additional dimensions were taken into account during the simulation experiments. The aspects of the performed analysis and benchmarking methods include various weighing methods (results obtained using entropy and standard deviation methods) and varied techniques of normalization of MCDA model input data. Comparative analyses showed the detailed influence of values of particular parameters on the final form and a similarity of the final rankings obtained by different MCDA methods.

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Actual existing multi-criteria decision-making (MCDM) methods yield results that may be questionable and unreliable. These methods very often ignore the issue of uncertainty and rank reversal paradox, which are fundamental and important challenges of MCDM methods. In response to these challenges, the Characteristic Objects Method (COMET) was developed. Despite it being immune to the rank reversal paradox, classical COMET is not designed for uncertain, decisional problems. In this paper, we propose to extend COMET using hesitant fuzzy set (HFS) theory. Hesitant fuzzy set theory is a powerful tool to express the uncertainty that derives from an expert comparing characteristic objects and identifying membership functions for each criterion domain. We present the theoretical foundations and principles of COMET, and we provide an illustrative example to show how COMET handles uncertain decision problems both practically and effectively.

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Multicriteria decision-making (MCDM) methods are concerned with the ranking of alternatives based on expert judgements made using a number of criteria. In the MCDM field, the distance-based approach is one popular method for obtaining a final ranking. The technique for order preference by similarity to the ideal solution (TOPSIS) is a commonly used example of this kind of MCDM method. The TOPSIS ranks the alternatives with respect to their geometric distance from the positive and negative ideal solutions. Unfortunately, two reference points are often insufficient, especially for nonlinear problems. As a consequence of this situation, the final result ranking is prone to errors, including the rank reversals phenomenon.This study proposes a new distance-based MCDM method: the characteristic objects method. In this approach, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, we have determined the domain and Fuzzy number set for all the considered criteria. The characteristic objects are obtained as the combination of the crisp values of all the Fuzzy numbers. The preference values of all the characteristic object are determined on the basis of the tournament method and the principle of indifference. Finally, the Fuzzy model is constructed and is used to calculate preference values of the alternatives, making it a multicriteria model that is free of rank reversal. The numerical example is used to illustrate the efficiency of the proposed method with respect to results from the TOPSIS method. The characteristic objects method results are more realistic than the TOPSIS results.

Abstract:There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision process. In such situations, we can observe an increasing importance of uncertainty. In this paper, the Multi-Criteria Decision-Making (MCDM) method called the Characteristic Objects Method (COMET) is extended to solve problems for Multi-Criteria Group Decision-Making (MCGDM) in a hesitant fuzzy environment. It is a completely new idea for solving problems of group decision-making under uncertainty. In this approach, we use L-R-type Generalized Fuzzy Numbers (GFNs) to get the degree of hesitancy for an alternative under a certain criterion. Therefore, the classical COMET method was adapted to work with GFNs in group decision-making problems. The proposed extension is presented in detail, along with the necessary background information. Finally, an illustrative numerical example is provided to elaborate the proposed method with respect to the support of a decision process. The presented extension of the COMET method, as opposed to others' group decision-making methods, is completely free of the rank reversal phenomenon, which is identified as one of the most important MCDM challenges.

A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the qth powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent flexibility. Due to the flexible nature of these Einstein operational laws, we introduce the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator, q-rung orthopair fuzzy Einstein ordered weighted averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator. We discuss certain properties of these operators, inclusive of their ability that the aggregated value of a set of q-ROFNs is a unique q-ROFN. By utilizing the proposed Einstein operators, this article describes a robust multi-criteria decision making (MCDM) technique for solving real-world problems. Finally, a numerical example related to integrated energy modeling and sustainable energy planning is presented to justify the validity and feasibility of the proposed technique.

Problems related to sustainable urban transport have gained in importance with the rapid growth of urban agglomerations. There is, therefore, a need to support decision-making processes in this area, a trend that is visible in the literature. Many methods have already been presented as a useful decision-making tool in this field. However, it is still a significant challenge to properly determine the relevance of the criteria because it is one of the most critical points of many presented techniques to solve decision problems. In this work, we propose two new approaches to determining the relevance of particular decision criteria effectively in sustainable transport problems. For this purpose, we examine a study case for the evaluation of electric bikes evaluated against eight criteria, which have been taken from earlier work. We calculate the relevance of each criterion using four different approaches and then evaluate their effectiveness using a reference ranking and popular multi-criteria decision analysis methods. The results are compared with each other by using similarity coefficients. Finally, we summarize the results obtained and set out further methods of development.