The symmetry property for the number of fuzzy subgroups of rectangle groups

A novel compact dual slant-polarized antenna with excellent pattern symmetry property for MIMO base station

Advances in Communication Technology and Application ◽

10.2495/cta140211 ◽

2014 ◽

Author(s):

Z. Zeng ◽

J.J. Huang ◽

Z.H. Song ◽

Q.Y. Zhang

Keyword(s):

Symmetry Property ◽

Base Station

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On the Radial Symmetry Property for Harmonic Functions

Russian Mathematics ◽

10.3103/s1066369x20100023 ◽

2020 ◽

Vol 64 (10) ◽

pp. 9-19

Author(s):

V. V. Volchkov ◽

Vit. V. Volchkov

Keyword(s):

Harmonic Functions ◽

Symmetry Property ◽

Radial Symmetry

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Image development in the framework of ξ –complex fuzzy morphisms

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201261 ◽

2021 ◽

pp. 1-13

Author(s):

Aneeza Imtiaz ◽

Umer Shuaib ◽

Abdul Razaq ◽

Muhammad Gulistan

Keyword(s):

Decision Making ◽

Comparative Analysis ◽

Fuzzy Sets ◽

Unit Disk ◽

Homomorphic Image ◽

Significant Role ◽

Original Form ◽

Mathematical Tool ◽

Fuzzy Subgroups ◽

Fundamental Theorems

The study of complex fuzzy sets defined over the meet operator (ξ –CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ –CFS and propose the notion of complex fuzzy subgroups defined over ξ –CFS (ξ –CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concepts of ξ –complex fuzzy homomorphism and ξ –complex fuzzy isomorphism between any two ξ –complex fuzzy subgroups and establish fundamental theorems of ξ –complex fuzzy morphisms. In addition, we effectively apply the idea of ξ –complex fuzzy homomorphism to refine the corrupted homomorphic image by eliminating its distortions in order to obtain its original form. Moreover, to view the true advantage of ξ –complex fuzzy homomorphism, we present a comparative analysis with the existing knowledge of complex fuzzy homomorphism which enables us to choose this particular approach to solve many decision-making problems.

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