Expanded hesitant fuzzy sets and group decision making: slides for FUZZ-IEEE 2017

[EN]We define expanded hesitant fuzzy sets, which incorporate all available information of the decision makers that provide the membership degrees that define a hesitant fuzzy set. We show how this notion relates to hesitant fuzzy set and extended hesitant fuzzy set. We define various scores for this setting, which generalize popular scores for hesitant fuzzy elements. Finally, a group decision making procedure is presented and illustrated with an example

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

The Selection of Investment Priorities using Expanded Dual Hesitant Fuzzy Sets

The concept of expanded dual hesitant fuzzy set is a concept that can be applied in decision-making problems. In decision-making problems, expanded dual hesitant fuzzy set can be applied to represent the opinions of multiple experts or stakeholders in a more elaborate manner. It enables decision-makers to provide more detailed information about their preferences and hesitancy

Modeling group assessments by means of hesitant fuzzy linguistic term sets

Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.Peer ReviewedPostprint (author's final draft

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

Bibliometric analysis of quality function deployment with fuzzy systems

Research on quality function deployment (QFD) with fuzzy systems has increased since the 2000s. The growing number of QFD applications with fuzzy systems indicates worldwide attention on this field of research. Then, two research questions arise: Are there some trends? And, are there some research gaps? This paper presents bibliometric analysis to answer those questions, performed on data from Scopus database, in a total output of 598 documents. Only articles and reviews were searched. China is the leading country in publication and international collaboration (207 published documents, more than a third of total). The main finding of analysis is the trend of QFD integration with fuzzy and multi-criteria decision-making (MCDM) methods. This could be observed with different applications as new product development, quality management, service quality, and supply chain management, to name a few.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(undefined

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

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