Premium
Strategies on admissible total orders over typical hesitant fuzzy implications applied to decision making problems
Author(s) -
Matzenauer Mônica,
Reiser Renata,
Santos Hélida,
Bedregal Benjamín,
Bustince Humberto
Publication year - 2021
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22374
Subject(s) - cardinality (data modeling) , multiple criteria decision analysis , fuzzy logic , mathematics , context (archaeology) , mathematical optimization , ranking (information retrieval) , negation , fuzzy set operations , fuzzy number , computer science , fuzzy set , artificial intelligence , data mining , paleontology , biology , programming language
Multi Expert‐Multi Criteria Decision Making (ME‐MCDM) problems have been well explored on hesitant fuzzy environments dealing with membership degrees as subsets which do not necessarily have the same cardinality. Admissible (total) orders collaborate by reducing the collapse in the ranking of alternatives related to preference relations. In such context, three classes of admissible orders are presented in a non‐restrictive way, integrating the concepts of linearity and cardinality and providing support to the comparison between two typical hesitant fuzzy elements. In the sense of hesitant fuzzy logic, the study of fuzzy operators and their main properties is extended considering the admissible linear orders. Namely, the typical hesitant fuzzy aggregation functions, negations and implication functions are discussed mainly related to their (iso/anti)tonicity properties w.r.t. these admissible orders. An algorithmic procedure is introduced illustrating our strategy to solve an ME‐MCDM problem, by selecting a Computer Integrating Manufacturing software and making use of the achieved theoretical results.