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This paper introduces a novel decision-making framework designed to enhance personalized support in Decision Support Systems (DSS). Existing methods often rely on single-dimensional modeling, which can introduce bias and uncertainty in criteria weighting. To address this, the study introduces a new approach for integrating subjective preferences with the multiple Expected Solution Points (ESPs) approach within the Characteristic Objects Method (COMET). This dual-dimensional approach tailors decision-making to align more closely with individual preferences and desired outcomes. Applied to the housing location selection problem, the proposed approach captures diverse user needs, delivering highly personalized and relevant recommendations. A comparative analysis with selected subjective weighting methods validates the stability and reliability of the multiple ESP-COMET model. By advancing personalization in decision support systems, this research offers a robust framework for more accurate and user-centered decision-making across complex scenarios.

pyMCMA is the Python implementation of a novel method for autonomous computation of the Pareto-front representation composed of efficient solutions distributed uniformly in terms of distances between neighbor Pareto solutions. pyMCMA supports scientific, i.e. objective, model analysis by providing preference-free Pareto front representation. pyMCMA seamlessly integrates independently developed substantive models. The computed Pareto-front, also for more than two criteria, is visualized by interactive parallel coordinate plot, as well as by charts of criteria pairs. Moreover, pyMCMA optionally exports the results for problems-specific analysis in the substantive model’s variables space. The pyMCMA functionality is illustrated by an analysis of China’s liquid fuel production model.

Data normalization is a fundamental part of preprocessing in decision-making problems. It enables aggregating and comparing different decision attributes using Multi-Criteria Decision Making (MCDM) methods. However, the choice of normalization technique significantly influences the final ranking. Different rankings are obtained using different normalization techniques for the same alternatives and methods. At the same time, the rank-reversal phenomenon is observed in many popular MCDM methods. This paper addresses the challenge of developing the MCDA method, which is rank-reversal free and solves the choosing normalization technique problem. We propose a new method called Compromise-COMET (C-COMET), which identifies the adaptive decision model based on many normalization techniques and finds a compromise solution. The Characteristic Objects METhod (COMET) has been modified to include a voting algorithm to assess characteristic objects. This approach is distinct from previous hybrid approaches, which integrated different MCDA methods with COMET since the main focus of this work is to obtain a compromise solution based on indirect voting. It means that instead of voting for the ranking of alternatives (like in the Copeland, Borda, or the Rank Position Method (RPM)), we vote for the preferences of characteristic objects. We identify a continuous assessment model free of the rank-reversal phenomenon in the result. Our investigation shows a study case where the Compromise-COMET method is considered with the TOPSIS method in detail. Afterward, we present more analysis for using C-COMET with Weighted Aggregated Sum Product ASSessment (WASPAS), COmbined COmpromise SOlution (COCOSO), MultiAttributive Ideal-Real Comparative Analysis (MAIRCA), and Measurement Alternatives and Ranking according to COmpromise Solution (MARCOS) methods to show the robustness of our proposal approach. The C-COMET algorithm models results with high values of weighted Spearman correlation and the weighted similarity (WS) coefficient, confirming our proposal’s accuracy.

This paper analyzes the behavior of the well-known Spearman's footrule distance (F-distance) to measure the distance between two rankings over the same set of objects. We show that F-distance is not invariant to labeling, and therefore, it suffers from a serious drawback for its use in applications. To circumvent this problem, we propose a new distance between rankings which is invariant under indexing (i.e., labeling) and appears as a good alternative to the direct use of F-distance between rankings, and also the invariant-under-indexing Kemeny's distance as well. We also show how our new distance can work with importance weights. Some simple examples are given to show the interest of our method with respect to the classical one based on F-distance and Kemeny's distance.

This paper looks into the extension of the pymcdm library, focusing on reference point-based techniques. It introduces the implementations of methods such as the Reference Ideal Method (RIM), Preference Ranking On the Basis of Ideal-average Distance (PROBID), and Election based on Relative Value Distances (ERVD). This update is intended to meet the increasing demand for solutions tailored to decision makers’ expertise and experience. Furthermore, it introduces techniques related to sensitivity analysis and weight comparison factors of criteria. By expanding this library, the range of MCDA/MCDM tools is broadened and further progress is encouraged in the use of expert knowledge and the implementation of compromise methods.

Multi-criteria decision-making/analysis is a vast field designed for solving decision-making problems. Due to the widespread use of many relevant MCDA/MCDM approaches and their frequent appearance in scientific papers, there is a particular gap regarding comprehensive software that should have relevant components. Therefore, this paper proposes a flexible library written in Python 3 for multi-criteria analysis/decision-making. It includes tools related to evaluating alternative options, determination of Pareto optimal solutions, determination of criteria relevance, comparative analysis, and visualization. The novelty that distinguishes the library from other software is the provision of a wide range of approaches, high performance, consistency of the software, and its small size. The research presented in this paper presents its high potential as a tool that decision-makers and domain experts can use in the decision-making process.

The aim of this paper is to present the use of an innovative approach based on MCDM methods as the main component of a consumer Decision Support System (DSS) by recommending the most suitable products among a given set of alternatives. This system provides a reliable recommendation to the consumer in the form of a compromise ranking constructed from the five MCDM methods: the hybrid approach TOPSIS-COMET, COCOSO, EDAS, MAIRCA, and MABAC. Each of the methods used contributes significantly to the final compromise ranking built with the Copeland strategy. Chosen MCDM methods were combined with the objective CRITIC weighting method, and their performance was presented on the illustrative example of choosing the most suitable mobile phone. A sensitivity analysis involving the rw and WS correlation coefficients was performed to determine the match between the compromise ranking of the candidates and the rankings provided by each MCDM method. Sensitivity analysis demonstrated that all investigated compromise candidate rankings show high convergence with the rankings provided by the particular MCDM methods. Thus, the performed study proved that the proposed approach shows high potential to be successfully used as a central component of DSS for recommending the most suitable product. Such DSS could be a universal and future-proof solution for e-commerce sites and websites, providing advanced product comparison capabilities in delivering a recommendation to the user as a final ranking of alternatives.

A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman’s rank correlation test assesses the statistical significance of two rankings sets.

Sustainable transportation has a significant impact on factors related to urban development and economic development. Therefore, much research is being undertaken to select the best strategies to manage sustainable transportation. Transportation requires a carefully designed method to manage the development of mobility modes in terms of the pollution they produce or the use of renewable energy sources. However, due to numerous preferences of decision-makers and data uncertainty problems, it is challenging to select the optimal strategy. In this paper, we focus on creating a framework for determining the best strategy for sustainable transportation management. For this purpose, T-spherical fuzzy graphs will be used, which, together with the combination of Laplacian Energy, can accurately represent decision-makers’ preferences in an uncertain environment. Due to the lack of limitations of T-spherical fuzzy graphs and its numerous membership functions, decision-makers can decide which factor seems most important for selecting the optimal sustainable transportation strategy. Additionally, due to the applicability, the SFS TOPSIS approach has been used in this approach. The obtained results demonstrate the high performance of the proposed approach and the applicability of the approach in management and sustainable transport problems.

The Pythagorean fuzzy sets conveniently capture unreliable, ambiguous, and uncertain information, especially in problems involving multiple and opposing criteria. Pythagorean fuzzy sets are one of the popular generalizations of the intuitionistic fuzzy sets. They are instrumental in expressing and managing hesitant under uncertain environments, so they have been involved extensively in a diversity of scientific fields. This paper proposes a new Pythagorean entropy for Multi-Criteria Decision-Analysis (MCDA) problems. The entropy measures the fuzziness of two fuzzy sets and has an influential position in fuzzy functions. The more comprehensive the entropy, the more inadequate the ambiguity, so the decision-making established on entropy is beneficial. The COmplex PRoportional ASsessment (COPRAS) method is used to tackle uncertainty issues in MCDA and considers the singularity of one alternative over the rest of them. This can be enforced to maximize and minimize relevant criteria in an assessment where multiple opposing criteria are considered. Using the Pythagorean sets, we represent a decisional problem solution by using the COPRAS approach and the new Entropy measure.

A graph is a tool for designing a system’s required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided ηζ network S(ηζΓ) and discussed their topology. In graph theory, there are a variety of invariants to study the topology of a network, but topological indices are designed in such a way that these may transform the graph into a numeric value. In this work, we study S(ηζΓ) via Zagreb connection indices. Due to their predictive potential for enthalpy, entropy, and acentric factor, these indices gain value in the field of chemical graph theory in a very short time. ηζΓ formed by ζ time repeated process which consists ηζ copies of graph Γ along with η2|V(Γ)|ζηζ−1 edges which used to join these ηζ copies of Γ. The free hand to choose the initial graph Γ for desired network S(ηζΓ) and its relation with chemical networks along with the repute of Zagreb connection indices enhance the worth of this study. These computations are theoretically innovative and aid topological characterization of S(ηζΓ).

In many physical models, internal energy will run out without external energy sources. Therefore, finding optimal energy sources and studying their behavior are essential issues. In this article, we study the following variational problem: Gϵ∗=sup∫ΩG(u)ϵq(x)dx:∥∇u∥Lp(.)≤ϵ,u=0 on ∂Ω, with the help of Γ-convergence, where G:R→R is upper semicontinuous, non zero in the L1 sense, 0≤G(u)≤c|u|q(.), Ω is a bounded open subset of Rn, n≥3, 1

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous.

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.

This paper aims to present an innovative approach based on two newly developed Multi-Criteria Decision-Making (MCDM) methods: COMET combined with TOPSIS and SPOTIS, which could be the basis for a decision support system (DSS) in the problem of selecting solar panels. Solar energy is one of the most promising and environmentally friendly energy sources because of the enormous potential of directly converting available solar radiation everywhere into electricity. Furthermore, ever-lower prices for photovoltaic systems make solar electricity more competitive with power from conventional energy sources, increasing interest in solar panels among companies and households. This fact generates the need for a user-friendly, objective, fully automated DSS to support the multi-criteria selection of solar panels. Both MCDM methods chosen for this purpose are rank-reversal-free and precise. First, the objective entropy weighting method was applied for determining criteria weights. Final rankings were compared by two ranking correlation coefficients: symmetrical rw and asymmetrical WS. Then the sensitivity analysis providing local weights of alternatives for decision criteria was performed. The obtained results prove the adequacy and practical usefulness of the presented approach in solving the problem of solar panels selection.