Construction of Typical Hesitant Triangular Norms regarding Xu-Xia-partial Order

Abstract

Fuzzy Sets theory has been applied in many fields to handle uncertainty, which can be reflected on the membership degree of the objects belonging to a set. Moreover, Hesitant Fuzzy Sets are useful whenever there is indecision among several possible values for the preferences over objects in the process of decision-making. In this sense, the aim of this work is to consider the notion of aggregation functions regarding Xu-Xia-partial order for typical hesitant fuzzy elements and to study Typical Hesitant Triangular Norms and some of the properties usually demanded to such operator.

On typical hesitant fuzzy automata

“…The ordering problem THFS and THFE have yet been studied in [31,32,35,36]. Now we propose a new relation on H based in the sup-combination, and we will show that this order generalizes the usual order of real numbers.…”

“…The set H 1 = {X ∈ H | #X = 1} is called of degenerate elements set. Several operators on H were proposed in [25,28,29,30,31,32,33]. In particular, Costa and Bedregal [23], have presented the inf-combination and sup-combination.…”

Typical Hesitant Fuzzy Sets: Evaluating Strategies in GDM Applying Consensus Measures

“…According with [30,Prop.1], (H, ≤XX ) is a complete lattice with the bottom and top elements given by 0 H = {0} and 1 H = {1}, respectively.…”

“…Since then, they have been studied, exploring the properties of hesitant fuzzy connectives, providing examples and investigating extensions from other fuzzy logic approaches. Then, some works came next, such as [5], [4], [30], [14], [20], [25] [43] and [40].…”