Integrating TOPSIS and ELECTRE-Ⅰ methods with cubic m-polar fuzzy sets and its application to the diagnosis of psychiatric disorders

Many real-world decision-making issues frequently involve competing sets of criteria, uncertainty, and inaccurate information. Some of these require the involvement of a group of decision-makers, where it is necessary to reduce the various available individual preferences to a single collective preference. To enhance the effectiveness of multi-criteria decisions, multi-criteria decision-making is a popular decision-making technique that makes the procedure more precise, reasonable, and efficient. The "Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)" and "Elimination and Choice Transforming Reality (ELECTRE)" are prominent ranking methods and widely used in the multi-criteria decision-making to solve complicated decision-making problems. In this study, two $m$-polar fuzzy set-based ranking methods are proposed by extending the ELECTRE-Ⅰ and TOPSIS approaches equipped with cubic $m$-polar fuzzy (C$m$PF) sets, where the experts provide assessment results on feasible alternatives through a C$m$PF decision matrix. The first proposed method, C$m$PF-TOPSIS, focuses on the alternative that is closest to a C$m$PF positive ideal solution and farthest away from the C$m$PF negative ideal solution. The Euclidean and normalized Euclidean distances are used to determine the proximity of an alternative to ideal solutions. In contrast, the second developed method is C$m$PF-ELECTRE-Ⅰ which uses an outranking directed decision graph to determine the optimal alternative, which entirely depends on the C$m$PF concordance and discordance sets. Furthermore, a practical case study is carried out in the diagnosis of impulse control disorders to illustrate the feasibility and applicability of the proposed methods. Finally, a comparative analysis is performed to demonstrate the veracity, superiority, and effectiveness of the proposed methods

Notes on soft sets and aggregation operators

[EN]Under uncertainty, traditional sets may not be sufficient to represent real-world phenomena, and fuzzy sets can provide a more flexible and natural approach. The concept of fuzzy sets has been widely used in various fields, including artificial intelligence, control theory, decision-making, and pattern recognition. Fuzzy sets can also be combined with other mathematical tools, such as probability theory, to provide a more comprehensive approach to uncertainty management. In these notes, we explore the concept of fuzzy sets under uncertainty, and their applications in various fields. We discuss the fundamental concepts of fuzzy sets, including fuzzy membership functions, fuzzy operations, and fuzzy relations. We also examine different types of uncertainty, including epistemic and aleatory uncertainty, and how fuzzy sets can be used to model and manage uncertainty in these cases

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (1/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

Bibliometric analysis of scientific production on methods to aid decision making in the last 40 years

Purpose: Multicriteria methods have gained traction in both academia and industry practices for effective decision-making over the years. This bibliometric study aims to explore and provide an overview of research carried out on multicriteria methods, in its various aspects, over the past forty-four years. Design/Methodology/Approach: The Web of Science (WoS) and Scopus databases were searched for publications from January 1945 to April 29, 2021, on multicriteria methods in titles, abstracts, and keywords. The bibliographic data were analyzed using the R bibliometrix package. Findings: This bibliometric study asserts that 29,050 authors have produced 20,861 documents on the theme of multicriteria methods in 131 countries in the last forty-four years. Scientific production in this area grows at a rate of 13.88 per year. China is the leading country in publications with 14.14%; India with 10.76%; and Iran with 8.09%. Islamic Azad University leads others with 504 publications, followed by the Vilnius Gediminas Technical University with 456 and the National Institute of Technology with 336. As for journals, Expert Systems With Applications; Sustainability; and Journal of Cleaner Production are the leading journals, which account for more than 4.67% of all indexed literature. Furthermore, Zavadskas E. and Wang J have the highest publications in the multicriteria methods domain regarding the authors. Regarding the most commonly used multicriteria decision-making methods, AHP is the most favored approach among the ten countries with the most publications in this research area, followed by TOPSIS, VIKOR, PROMETHEE, and ANP. Practical implications: The bibliometric literature review method allows the researchers to explore the multicriteria research area more extensively than the traditional literature review method. It enables a large dataset of bibliographic records to be systematically analyzed through statistical measures, yielding informative insights. Originality/value: The usefulness of this bibliometric study is summed in presenting an overview of the topic of the multicriteria methods during the previous forty-four years, allowing other academics to use this research as a starting point for their research

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (3/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (2/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

Enhancing the cosmetics industry sustainability through a renewed sustainable supplier selection model

The cosmetics industry requires a long-term sustainable strategy to balance its continuously growing trend worldwide and its resources consumption. In this view, the suppliers' selection process is gaining more attention affecting products' overall sustainability. The objective of this contribution is hence to develop and validate the Cosmetics Sustainable Supplier Selection (C-SSS) model allowing the selection of sustainable suppliers for the cosmetic industry, evaluating them in an objective and balanced manner. The model was built relying on both scientific and grey literature, by incorporating the characteristics of existing SSS models usually used separately. The C-SSS enabled to integrate the EMM approach (to reduce the subjectivity), the ANP approach (to evaluate criteria interconnections), and the TOPSIS and ELECTRE models (to create a hybrid compensation model) to support managers in objectively selecting the most sustainable suppliers. The C-SSS model was applied and validated through an industrial use case in a cosmetics Italian company

A systematic literature review of soft set theory

[EN] Soft set theory, initially introduced through the seminal article ‘‘Soft set theory—First results’’ in 1999, has gained considerable attention in the field of mathematical modeling and decision-making. Despite its growing prominence, a comprehensive survey of soft set theory, encompassing its foundational concepts, developments, and applications, is notably absent in the existing literature. We aim to bridge this gap. This survey delves into the basic elements of the theory, including the notion of a soft set, the operations on soft sets, and their semantic interpretations. It describes various generalizations and modifications of soft set theory, such as N-soft sets, fuzzy soft sets, and bipolar soft sets, highlighting their specific characteristics. Furthermore, this work outlines the fundamentals of various extensions of mathematical structures from the perspective of soft set theory. Particularly, we present basic results of soft topology and other algebraic structures such as soft algebras and sigma-algebras. This article examines a selection of notable applications of soft set theory in different fields, including medicine and economics, underscoring its versatile nature. The survey concludes with a discussion on the challenges and future directions in soft set theory, emphasizing the need for further research to enhance its theoretical foundations and broaden its practical applications. Overall, this survey of soft set theory serves as a valuable resource for practitioners, researchers, and students interested in understanding and utilizing this flexible mathematical framework for tackling uncertainty in decision-making processes

Similarity Multi Criteria Decision Making Using Normalized 3 – Polar ELECTRE I and Fuzzy 3 – Polar Dombi Arithmatic AOs (Case Study of Determining Manufacture Location)

The m-Polar fuzzy set is a set that not only overcomes data ambiguity, but can also handle multi-polar, multi-attribute, and multi-criteria information. The m-Polar fuzzy set is useful in describing uncertainty in multi-attribute decision-making. One of the techniques used in decision-making is the ELECTRE I method. The ELECTRE I method plays a role in conducting pairwise comparisons between alternatives given by the decision-maker, where alternatives, criteria, and weights are given by the decision-maker. Furthermore, the ranking results from the ELECTRE I method will be compared with the mF Dombi Weighted Averaging (m-FDWA) aggregation operator with the help of the arithmetic operator. The purpose of this study was to compare the ranking results of the mF ELECTRE I, and the normalized and non-normalized m-FDWA arithmatic methods. The data used is secondary data related to site selection for global manufacturing with 20 alternative countries (country) and 8 criteria. The results showed that the best alternative to the normalized mF ELECTRE I and m-FDWA methods was country 14. While the m-FDWA arithmetic method without normalization resulted in country 3 as the best alternative. The effectiveness test was applied to m-FDWA arithmetic method, both normalized and without normalization to test the validity of the model so that it can be seen that normalization does not affect the validity of the model

A systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version