New measure of circular intuitionistic fuzzy sets and its application in decision making

Changlin Xu; Yaqing Wen; Changlin Xu; Yaqing Wen

doi:10.3934/math.20231226

AIMS Mathematics

2023, Volume 8, Issue 10: 24053-24074. doi: 10.3934/math.20231226

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Research article Special Issues

New measure of circular intuitionistic fuzzy sets and its application in decision making

Changlin Xu ^{1,2
,
,},
Yaqing Wen ¹

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, China
2.
The Key Laboratory of Intelligent Information and Big Data Processing of Ningxia Province, North Minzu University, Yinchuan, Ningxia 750021, China

Received: 24 February 2023 Revised: 01 July 2023 Accepted: 30 July 2023 Published: 08 August 2023
MSC : 28E10, 90B50, 91B06

Circular intuitionistic fuzzy sets are further extensions of intuitionistic fuzzy sets with a stronger ability to express uncertain information than intuitionistic fuzzy sets. This paper firstly defines a new distance measure for circular intuitionistic fuzzy sets based on the theory of circular intuitionistic fuzzy sets, considering the information of four aspects: membership degree, non-membership degree, radius and the assignment of hesitation degree, and proves that the new distance satisfies the distance measure conditions. Secondly, by constructing a manual testing framework, the new distance is analyzed in comparison with the existing distance metric to show the rationality of the new method. Finally, the method is applied to fuzzy multi-criteria decision making to further demonstrate the effectiveness and practicality of the method.
- circular intuitionistic fuzzy set,
- distance,
- hesitation degree,
- fuzzy multi-criteria decision making
Citation: Changlin Xu, Yaqing Wen. New measure of circular intuitionistic fuzzy sets and its application in decision making[J]. AIMS Mathematics, 2023, 8(10): 24053-24074. doi: 10.3934/math.20231226

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Abstract

Circular intuitionistic fuzzy sets are further extensions of intuitionistic fuzzy sets with a stronger ability to express uncertain information than intuitionistic fuzzy sets. This paper firstly defines a new distance measure for circular intuitionistic fuzzy sets based on the theory of circular intuitionistic fuzzy sets, considering the information of four aspects: membership degree, non-membership degree, radius and the assignment of hesitation degree, and proves that the new distance satisfies the distance measure conditions. Secondly, by constructing a manual testing framework, the new distance is analyzed in comparison with the existing distance metric to show the rationality of the new method. Finally, the method is applied to fuzzy multi-criteria decision making to further demonstrate the effectiveness and practicality of the method.

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