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Symmetry 2018, 10(7), 251; https://doi.org/10.3390/sym10070251

Complex Fuzzy Geometric Aggregation Operators

1
School of Electronics and Communication Engineering, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China
2
School of Information Science and Engineering, Xiamen University, Xiamen 361005, China
3
School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Received: 15 June 2018 / Revised: 25 June 2018 / Accepted: 28 June 2018 / Published: 2 July 2018
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Abstract

A complex fuzzy set is an extension of the traditional fuzzy set, where traditional [0,1]-valued membership grade is extended to the complex unit disk. The aggregation operator plays an important role in many fields, and this paper presents several complex fuzzy geometric aggregation operators. We show that these operators possess the properties of rotational invariance and reflectional invariance. These operators are also closed on the upper-right quadrant of the complex unit disk. Based on the relationship between Pythagorean membership grades and complex numbers, these operators can be applied to the Pythagorean fuzzy environment. View Full-Text
Keywords: complex fuzzy sets; aggregation operator; complex fuzzy geometric operators; rotational invariance; reflectional invariance complex fuzzy sets; aggregation operator; complex fuzzy geometric operators; rotational invariance; reflectional invariance
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Bi, L.; Dai, S.; Hu, B. Complex Fuzzy Geometric Aggregation Operators. Symmetry 2018, 10, 251.

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