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Article

Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

1
Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2
Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea
3
Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
4
BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(11), 215; https://doi.org/10.3390/math6110215
Received: 6 October 2018 / Revised: 20 October 2018 / Accepted: 21 October 2018 / Published: 24 October 2018
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. View Full-Text
Keywords: intuitionistic fuzzy value; intuitionistic fuzzy set; score function; centroid; aggregation intuitionistic fuzzy value; intuitionistic fuzzy set; score function; centroid; aggregation
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MDPI and ACS Style

Liu, X.; Kim, H.S.; Feng, F.; Alcantud, J.C.R. Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators. Mathematics 2018, 6, 215. https://doi.org/10.3390/math6110215

AMA Style

Liu X, Kim HS, Feng F, Alcantud JCR. Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators. Mathematics. 2018; 6(11):215. https://doi.org/10.3390/math6110215

Chicago/Turabian Style

Liu, Xiaoyan, Hee Sik Kim, Feng Feng, and José Carlos R. Alcantud. 2018. "Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators" Mathematics 6, no. 11: 215. https://doi.org/10.3390/math6110215

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