Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

Abstract

Atanassov’s intuitionistic fuzzy sets extend the notion of fuzzy sets. In addition to Zadeh’s membership function, a non-membership function is also considered. Intuitionistic fuzzy values play a crucial role in both theoretical and practical progress of intuitionistic fuzzy sets. This study introduces and explores various types of centroid transformations of intuitionistic fuzzy values. First, we present some new concepts for intuitionistic fuzzy values, including upper determinations, lower determinations, spectrum triangles, simple intuitionistic fuzzy averaging operators and simply weighted intuitionistic fuzzy averaging operators. With the aid of these notions, we construct centroid transformations, weighted centroid transformations, simple centroid transformations and simply weighted centroid transformations. We provide some basic characterizations regarding various types of centroid transformations, and show their difference using an illustrating example. Finally, we focus on simple centroid transformations and investigate the limit properties of simple centroid transformation sequences. Among other facts, we show that a simple centroid transformation sequence converges to the simple intuitionistic fuzzy average of the lower and upper determinations of the first intuitionistic fuzzy value in the sequence.

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

“…A more general form of this aggregation operator was given in [49]. Liu et al 50 also developed centroid transformations of IFVs based on this notion.…”

A Study on Hypergraph Representations of Complex Fuzzy Information

“…Let {(μ 1 e iθ 1 ,ν 1 e iφ 1 ), (μ 2 e iθ 2 ,ν 2 e iφ 2 ), · · · , (μ l e iθ l ,ν l e iφ l )} be the set of complex numbers such that the corresponding partial hypergraphs H (μ 1 e iθ 1 ,ν 1 e iφ 1 ) , H (μ 2 e iθ 2 ,ν 2 e iφ 2 ) , · · · , H (μ l e iθ l ,ν l e iφ l ) are non-empty. 5. Then, f ss (H) = {(μ 1 e iθ 1 ,ν 1 e iφ 1 ), (μ 2 e iθ 2 ,ν 2 e iφ 2 ), · · · , (μ l e iθ l ,ν l e iφ l )} and cor(H) = { H (μ 1 e iθ 1 ,ν 1 e iφ 1 ) , H (μ 2 e iθ 2 ,ν 2 e iφ 2 ) , · · · , H (μ l e iθ l ,ν l e iφ l ) } are subsequence and subcore set of H, respectively.…”

“…Progress on the investigation of IFSs and related extensions of the FS concept continues to be made. Liu et al [5] introduced different types of centroid transformations of IF values. Feng et al [6] defined various new operations for generalized IF soft sets.…”

q-Rung Orthopair Fuzzy Hypergraphs with Applications

“…Applications of IFSs appear in various fields, including medical diagnosis, optimization problems, and decision-making. Recently, Liu et al [3] introduced and explored various types of centroid transformations of IF values. Furthermore, Feng et al [4] defined two different types of generalized IF soft subsets and various new operations for generalized IF soft sets.…”