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Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

Title
Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators
Author
김희식
Keywords
intuitionistic fuzzy value; intuitionistic fuzzy set; score function; centroid; aggregation
Issue Date
2018-10
Publisher
MDPI
Citation
MATHEMATICS, v. 6, no. 11, Article no. 215
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.
URI
https://www.mdpi.com/2227-7390/6/11/215https://repository.hanyang.ac.kr/handle/20.500.11754/120253
ISSN
2227-7390
DOI
10.3390/math6110215
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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