Decision support systems (DSS) are currently developing rapidly and are increasingly used in various fields. More often, those systems are inseparable from information-based systems and computer systems. Therefore, from a methodical point of view, the algorithms implemented in the DSS play a critical role. In this aspect, multi-criteria decision support (MCDA) methods are widely used. As research progresses, many MCDA methods and algorithms for the objective identification of the significance of individual criteria of the MCDA models were developed. In this paper, an analysis of available objective methods for criteria weighting is presented. Additionally, the authors presented the implementation of the system that provides easy and accessible weight calculations for any decision matrix with the possibility of comparing results of different weighting methods. The results of weighting methods were compared using carefully selected similarity coefficients to emphasise the correlation of the resulting weights. The performed research shows that every method should provide distinctive weights considering input data, emphasising the importance of choosing the correct method for a given multi-criteria decision support model and DSS.

In recent years, multi-criteria decision support methods have become widely used research tools by both scientists and practitioners. Theoretical works involving new multi-criteria methods and developments of existing methods immediately find applications in areas of business practice. This paper attempts to sort out the areas of application of MCDA methods. For this purpose, the relevant literature from 2018–2023 was reviewed. The inclusion selection criteria were defined as addressing multi-criteria practical issues, open accessibility, comprehensive research methodology and findings, and the use of an MCDA method in the evaluation process. Detailed research identified that the main areas of use of MCDA methods are healthcare, energy management, supplier selection, and transportation. Due to the timeliness and importance of the problem, a detailed study of the use of MCDA methods in sustainability issues was separated. The paper contributes contributions to both theory and economic practice. The article provides a series of recommendations both on the methodological side of the problems to be solved and shows the practical prism of individual decision models, offering ready-to-use decision models, and providing a comprehensive review of recent MCDA advancements, fostering informed and reliable decision-making. Additionally, this review sheds light on the latest developments in MCDA, emphasizing trends in Decision Support Systems (DSS) and prominent application areas in contemporary research.

In multi-criteria decision-making (MCDM), decision-makers face increasing complexity and the need for enhanced tools to facilitate informed and well-aligned decision outcomes. A critical challenge in MCDM is the determination of criteria weights, which significantly influence the final ranking of alternatives. While recent approaches aim to eliminate the need for explicit weight assignment, certain decision contexts necessitate their inclusion. This study introduces two novel coefficients, Rank Stability (RS) and Balance Point (BP), designed to provide deeper insights into the decision problem and its solution properties. Rank Stability quantifies the robustness of a solution against perturbations, while Balance Point evaluates the conditioning of the solution within the problem’s structure. The decision problem is defined by a set of alternatives and criteria, where modifications to alternatives require a reassessment of the decision model. To examine the properties of these coefficients, this study employs simulation experiments utilizing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods, alongside case-based analyses demonstrating their practical applications. Additionally, extreme cases of RS and BP values are explored to enhance interpretability for decision-makers. A real-world decision problem is further analyzed to illustrate the applicability of these coefficients and introduce a novel framework for comparing MCDM methodologies. This approach facilitates a more systematic and comprehensive assessment of MCDM methods, contributing to the advancement of decision-support tools.

The ever-increasing demand for high-quality solutions drives research toward more sophisticated decision-making solutions. In the field of decision making, the ability to solve complex real-world problems is of paramount importance. To this end, fuzzy sets are used, which offer the possibility of incorporating uncertainty into the values describing decision options. This study focuses on Pythagorean fuzzy sets, an extension of classical fuzzy sets, providing even more tools for modeling real-world problems by presenting a distance measure for these specific sets. A verification of the characteristics of the proposed distance measure has been carried out, proving its validity. The proposed measure is characterized by a more straightforward formula and thus simplifies the calculations. Furthermore, to confirm its usability, a multi-criteria decision-making methodology is presented, the results of which are compared with two multi-criteria decision-making methods, namely, PF-TOPSIS and PF-VIKOR, and another distance measure previously presented in the literature. The comparative analysis highlights lower variability in terms of preference values calculated using the proposed distance measure, which confirms the stability and reliability of the newly proposed distance measure while maintaining low computational complexity. Moreover, a high correlation with rankings calculated using PF-TOPSIS ensures its utility in terms of decision making.

The extension of intuitionistic fuzzy sets (IFS) to Pythagorean fuzzy sets (PFS) is a significant advancement, addressing the inherent limitations of IFS. This study introduces a novel entropy measure specifically designed for Pythagorean fuzzy sets, establishing its axiomatic definition and presenting key properties. Decision making guided by entropy is advantageous, as it effectively mitigates ambiguity with increasing entropy values. Furthermore, a numerical example is provided to facilitate a comparative assessment of our newly introduced entropy measure in contrast to existing PFS entropy measures. The validation of our findings is achieved through the application of the COPRAS method, which determines decision outcomes based on a multitude of influencing factors. Notably, the determination of weights in this method is underpinned by the utilization of our innovative entropy measure.