An approach for consensual analysis on Typical Hesitant Fuzzy Sets via extended aggregations and fuzzy implications based on admissible orders

Abstract

Typical Hesitant Fuzzy Logic (THFL) is founded on the theory of Hesitant Fuzzy Sets, which consider as membership degrees the finite and non-empty subsets of the unit interval, called Typical Hesitant Fuzzy Elements (THFE). THFL provides the modelling for situations where there exists not only data uncertainty, but also indecision or hesitation among experts about the possible values for preferences regarding collections of objects. In order to reduce the information collapse for comparison and/or ranking of alternatives in the preference relationships, this thesis develops new ideas on THFL connectives, investigated under the scope of three admissible orders. In particular, properties of negations and aggregations are studied, as t-norms and OWA operators, with special interest in the axiomatic structures defining the implications and preserving their algebraic properties and representability. As the main contribution, we present a model that formally builds consensus measures on THFE through extended aggregation functions and fuzzy negation, using admissible orders for comparison and further, differentiating an analysis of consistency over preference matrices. Main theoretical results are submitted to multiple expert and mutiple criteria decision making problems.