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This paper presents an original and comprehensive investigation into the Taxonomic Measure of Development (TMD), introduced by Hellwig in 1968, enriching both its theoretical foundations and practical applications. It provides an overview of various variants of the Hellwig method, including their extensions and applications, while also exploring recent trends across multiple research domains. Primarily developed as a method for multidimensional analysis, TMD has evolved into a pivotal tool in multi-criteria decision-making. It is widely used for evaluating and ranking alternatives, particularly in the analysis of complex socio-economic phenomena and decision-making scenarios involving multiple criteria. This study systematically reviews the original algorithm and its subsequent extensions and modifications, including adaptations for fuzzy sets, intuitionistic fuzzy sets, and interval-valued fuzzy sets. Furthermore, it explores an integrated multi-criteria approach based on Hellwig's method and its practical applications across various domains. This paper introduces an original approach by conducting a detailed, step-by-step analysis of the TMD framework. This process-oriented analysis is a novel contribution that sets this study apart from typical reviews based on statistical or bibliometric data. By examining key steps in the TMD framework—such as data collection, criterion weighting, data normalization, ideal value determination, distance calculation, and normalization factor—this paper highlights the method's versatility in addressing complex, real-world decision-making problems. Although similar to the widely used Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method in its reliance on distance to evaluate alternatives, Hellwig's approach is unique in focusing exclusively on proximity to an ideal solution, without considering distance from a negative ideal. This distinctive emphasis has led to numerous adaptations and extensions that address specific issues such as criterion dependencies, uncertainty, and rank reversal. The findings underscore the continued relevance of the Hellwig method, its recent extensions, and its growing international recognition. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making methods based on reference points and distances from them are essential for evaluating alternatives across multiple criteria. These methods provide structured approaches to comparing and ranking alternatives relative to specified reference points. The main objective of this paper is to present the Multi-Criteria Method Integrating Distances to Ideal and Anti-ideal Points (MIDIA), which, through a weighted system, allows for the consideration of balance and asymmetry in assessing alternatives based on their distances from the ideal and anti-ideal points. As a multi-criteria algorithm, MIDIA is user-friendly and reflects the human mind's natural tendency to assess objects based on fundamental concepts—comparison with the ideal solution and the anti-ideal solution—that are familiar from everyday experiences and provide valuable insights from a behavioral perspective. Moreover, the proposed method can be seen as an extension of Hellwig's approach, designed to facilitate the ranking of alternatives based on two reference points: the ideal point and the anti-ideal point, measuring the distance between the alternative and the ideal point and the distance between the ideal and anti-ideal points. The MIDIA method integrates elements from both TOPSIS and VIKOR, by incorporating the structure of TOPSIS and the compromise perspective of VIKOR, offering a balanced approach to multi-criteria decision-making by focusing on the distances from ideal and anti-ideal points. Illustrative examples are given to demonstrate the usability of the proposed tool in situations where the decision-maker has asymmetrical preferences concerning the importance of ideal and anti-ideal points in ranking alternatives. Moreover, the MIDIA method is applied to one of the Sustainable Development Goals, in the area of education (SDG4), to obtain the rankings of EU member countries in 2022. The results obtained using the MIDIA method were compared with those obtained using the TOPSIS and VIKOR approaches. The study concludes that the ranking of alternatives depends on the coefficients of the importance of the distances to reference points and the data setup. [ABSTRACT FROM AUTHOR]

Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be found. One involves normalization before calculating the entropy values, while the second does not. This paper investigates the normalization effect for entropy-based weights and Hellwig's method. To compare the influence of various normalization methods in both the EWM and Hellwig's method, a study evaluating the sustainable development of EU countries in the education area in the year 2021 was analyzed. The study used data from Eurostat related to European countries' realization of the SDG 4 goal. It is observed that vector normalization and sum normalization did not change the entropy-based weights. In the case study, the max–min normalization influenced EWM weights. At the same time, these weights had only a very weak impact on the final rankings of countries with respect to achieving the SDG 4 goal, as determined by Hellwig's method. The results are compared with the outcome obtained by Hellwig's method with equal weights. The simulation study was conducted by modifying Eurostat data to investigate how the different normalization relationships discovered among the criteria affect entropy-based weights and Hellwig's method results. [ABSTRACT FROM AUTHOR]

Introduction: The imbalance of external and internal forces acting on the lower eyelid can result in entropion and ectropion, both of which cause ocular irritation and loss of proper eye protection. Potential complications of untreated cases include recurrent inflammation of the conjunctiva and cornea, conjunctival neovascularization, corneal abrasion or perforation, and ultimately even loss of vision. Although various surgical techniques are used to address this problem, their long-term outcome and effectiveness are still under discussion. Aim: To evaluate outcomes of surgery for entropion and ectropion, including a modified Wheeler's method for entropion correction. Methods: A non-comparative study (prospective and retrospective groups) included 100 patients operated on in two university hospitals' plastic surgery departments for lower eyelid entropion or ectropion, following formal ethics approval. The prospective group included 50 patients assessed preoperatively and at 3 and 12 months postoperatively. The retrospective group was comprised of 50 patients (2012-2018), whose preoperative documentation and clinical examinations were analyzed. The main outcome measures were change between pre- and postoperative patient-reported symptoms (VAS scale), ectropion/entropion grading scale (EGS/EnGS), quality of life (WHOQOL-BREF), and occurrence of complications. Results: The differences in the severity of all symptoms before and after surgery evaluated with the VAS scale were statistically significant in both groups (p <0.05). We observed 6 recurrences (12%) in the prospective group and 9 (18%) in the retrospective group, with minor complications. Very good functional and esthetic postoperative results were confirmed in 70% (79) of the whole group and in 13 patients (81.3%) treated with the modified Wheeler's method. In the prospective group, the Mann--Whitney U test for dependent variables revealed significant improvement in the somatic, psychological, and environmental domains, with no significant change in the social relationships domain. Conclusions: The results following entropion/ectropion surgery prove the effectiveness of the methods used. Complementing them with the modified Wheeler's method brought an increase in the number of very good outcomes. Surgery of lower eyelid malposition contributed to reduced symptoms and improved quality of life. The rates of postoperative sequelae were low. [ABSTRACT FROM AUTHOR]

One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig's method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating the concept of entropy, weights are determined based on their information content represented by the matrix data. The Mahalanobis distance is employed to address interdependencies among criteria, contributing to the improved performance of the proposed framework. To illustrate the relevance and effectiveness of the extended H_EM method, this study utilizes it to assess the progress toward achieving Sustainable Development Goal 4 of the 2030 Agenda within the European Union countries for education in the year 2021. Performance comparison is conducted between results obtained by the extended Hellwig's method and its other variants. The results reveal a significant impact on the ranking of the EU countries in the education area, depending on the choice of distance measure (Euclidean or Mahalanobis) and the system of weights (equal or entropy-based). Overall, this study highlights the potential of the proposed method in addressing complex decision-making scenarios with interdependent criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of defining the weights in multiple criteria decision‐making analysis. In particular, we analyze if weights determined by decision makers (DMs) using the classic analytic hierarchy process (AHP) approach can be reproduced using more straightforward direct linguistic weights declarations (DLWD). Using the dataset from an online decision‐making experiment, we analyze the concordance of systems of weights obtained by DMs from AHP and DLWD. Applying optimization models, we check if the discrepancies between the AHP and DLWD weights result from (a) inefficiently declared mixes of linguistic labels in the symmetrically distributed scale or (b) using the unbalanced linguistic term set by DMs. The main findings are that the systems of weights obtained by DMs in the experiment from AHP and DLWD differ significantly. While using DLWD, most DMs defined criteria ranks contradictory to those resulting from AHP. They avoided extensive use of extreme labels from the 7‐point scale. The optimization results show that DLWD based on the symmetric scale might produce the most similar weights to AHP if a full range of linguistic terms was used, not only the intermediate ones. The differences in DMs' cognitive profiles seem not to affect the results. [ABSTRACT FROM AUTHOR]

In this paper we propose a multi-criteria model based on the fuzzy preferences approach which can be implemented in the prenegotiation phase to evaluate the negotiations packages. The applicability of some multi-criteria ranking methods were discussed for building a scoring function for negotiation packages. The first one is Simple Additive Weighting (SAW) technique which determines the sum of the partial satisfactions from each negotiation issue and aggregate them using the issue weights. The other one is Distance Based Methods (DBM), with its extension based on the distances to ideal or anti-ideal package, i.e. the TOPSIS procedure. In our approach the negotiator's preferences over the issues are represented by fuzzy membership functions and next a selected multi-criteria decision making method is adopted to determine the global rating of each package. The membership functions are used here as the equivalents of utility functions spread over the negotiation issues, which let us compare different type of data. One of the key advantages of the approach proposed is its usefulness for building a general scoring function in the ill-structured negotiation problem, namely the situation in which the problem itself as well as the negotiators preferences cannot be precisely defined, the available information is uncertain, subjective and vague. Secondly, all proposed variants of scoring functions produce consistent rankings, even though the new packages are added (or removed) and do not result in rank reversal.

This article presents a relatively straightforward theoretical framework about distributive justice with applications. It draws on a few key concepts of Sociological Game Theory (SGT). SGT is presented briefly in section 2. Section 3 provides a spectrum of distributive cases concerning principles of equality, differentiation among recipients according to performance or contribution, status or authority, or need. Two general types of social organization of distributive judgment are distinguished and judgment procedures or algorithms are modeled in each type of social organization. Section 4 discusses briefly the larger moral landscapes of human judgment – how distribution may typically be combined with other value into consideration. The article suggests that Rawls, Elster, and Machado point in this direction. Finally, it is suggested that the SGT framework presented provides a useful point of departure to systematically link it and compare the Warsaw School of Fair Division, Rawls, and Elster, among others.