Centroid transformations of intuitionistic fuzzy values based on aggregation operators
type: Item
instance of: scholarly article
title: Centroid transformations of intuitionistic fuzzy values based on aggregation operators
zbMATH Open document ID: 1400.68224
author: Hee Sik Kim
author: Feng Feng
author: Xiaoyan Liu
author: J. C. R. Alcantud
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 68T37
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 6994818
zbMATH Keywords: intuitionistic fuzzy value
zbMATH Keywords: intuitionistic fuzzy set
zbMATH Keywords: score function
zbMATH Keywords: centroid
zbMATH Keywords: aggregation
MaRDI profile type: Publication
full work available at URL: math6110215
OpenAlex ID: W2898109359
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Wikidata QID: Q129049309
DOI: 10.3390/MATH6110215
description: scientific article; zbMATH DE number 6994818