A contribution to consensus modeling in decision-making by means of linguistic assessments

Decision-making is an active field of research. Specifically, in recent times, a lot of contributions have been presented on decision-making under linguistic assessments. To tackle this kind of processes, hesitant fuzzy linguistic term sets have been introduced to grasp the uncertainty inherent in human reasoning when expressing preferences. This thesis introduces an extension of the set of hesitant fuzzy linguistic term sets to capture differences between non-compatible assessments. Based on this extension, a distance between linguistic assessments is defined to quantify differences between several opinions. This distance is used in turn to present a representative opinion from a group in a decision-making process. In addition, different consensus measures are introduced to determine the level of agreement or disagreement within a decision-making group and are used to define a decision maker’s profile to keep track of their dissension with respect to the group as well as their level of hesitancy. Furthermore, with the aim of allowing decision makers to choose the linguistic terms that they feel more comfortable with, the concept of free double hierarchy hesitant fuzzy linguistic term set is developed in this thesis. Finally, a new approach of the TOPSIS methodology for processes in which the assessments are given by means of free double hierarchy hesitant fuzzy information is presented to rank alternatives under these circumstances.Postprint (published version

Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as H, as well as the action of H-automorphisms which are defined over the set of all finite non-empty subsets of the unitary interval. In order to do so, the partial order ≤H, based on α-normalization, is introduced, leading to a comparison based on selecting the greatest membership degrees of the related fuzzy sets. Additionally, the idea of interval representation is extended to the context of typical hesitant aggregation functions named as the H-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the H-conjugate functions over such operators. © 2013 Elsevier Inc. All rights reserved.Peer Reviewe

A Historical Account of Types of Fuzzy Sets and Their Relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Perceptual maps to aggregate information from decision makers

Understanding different perceptions of human being when using linguistic terms is a crucial issue in human-machine interaction. In this paper, we propose the concept of perceptual maps to model human opinions in a group decision-making context. The proposed approach considers a multi-granular structure using unbalanced hesitant linguistic term sets. An illustrative case is presented in the location decisions made by multinationals enterprises of the energy sector within the European smart city context.This research was supported partly by the INVITE research project (TIN2016- 80049-C2-1-R and TIN2016-80049-C2-2-R), funded by the Spanish Ministry of Science and Information Technology and the European Union Horizon 2020 Research and Innovation Programme, under the grant agreement No 731297.Postprint (published version

A qualitative approach for aggregating people's perceptions

The concept of perceptual map is introduced in this paper to capture the semantics of linguistic assessments of an individual in a qualitative reasoning scenario, concretely in hesitant fuzzy linguistic term sets. In addition, the projected perceptual map is considered to provide a space to aggregate different perceptual maps. Qualitative distances and measures of centrality and agreement or consensus are revised based on this projected perceptual map.This research has been partially supported by the PERCEPTIONS R. P. (PID2020-114247GB-I00), funded by the Spanish Ministry of Science and Information Technology.Peer ReviewedPostprint (published version