On admissible total orders for typical hesitant fuzzy consensus measures

Abstract

In this paper, we discussconsensus measures for typical hesitant fuzzy elements (THFE), which are the finite and nonempty fuzzy membership degrees under the scope of typical hesitant fuzzy sets (THFS). In our approach, we present a model that formally constructs consensus measures by means of aggregations functions, fuzzy implication-like functions and fuzzy negations, using admissible orders to compare the THFE, and also providing an analysis of consistency on them. Our theoretical results are applied into a problem of decision making with multicriteria illustrating our methodology to achieve consensus in a group of experts working with THFS.

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

“…This admissible H, f A -orders is a family of total orders that refine the partial H, ≤ RH -order. The theorem presented below, can be seen in with more details in the thesis and in [Matzenauer et al 2021b].…”

“…This first consensus measures method CC AI is based on a typical hesitant extended aggregation function A and an H, -implication I. The theorem presented below, can be seen with more details in the thesis and in [Matzenauer et al 2021b]. Theorem 4.2 Let A be an extended H, -aggregation function satisfying some aggregations properties and I be an H, -implication verifying some implications properties.…”

“…is an H, , 0 H , 1 H -valued consensus measure on H, This second method, CC min,I -consensus model, considers the minimum typical hesitant aggregation (T min = min) and an H, -implication I, and is presented with more details in the thesis and in [Matzenauer et al 2021b].…”

“…• Hesitant Fuzzy Sets (HFS), proposed by [Torra and Narukawa 2009] as another extension for fuzzy sets, in which the membership degree of an hesitant fuzzy set is also given as a subset of [0,1].…”