Correlation coefficient of T-spherical type-2 hesitant fuzzy sets and their applications in clustering analysis

2021 ◽  
Author(s):  
Şerif Özlü ◽  
Faruk Karaaslan
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Clustering Analysis ◽  
Hesitant Fuzzy Sets ◽  
Spherical Type

scholarly journals Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-34
Author(s):  
Tahir Mahmood ◽  
Zeeshan Ali ◽  
Harish Garg ◽  
Lemnaouar Zedam ◽  
Ronnason Chinram
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Clustering Algorithm ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Hesitant Fuzzy Sets ◽  
Operational Laws ◽  
Special Cases ◽  
Entropy Measures

The theory of complex dual type-2 hesitant fuzzy sets (CDT-2HFSs) is a blend of two different modifications of fuzzy sets (FSs), called complex fuzzy sets (CFSs) and dual type-2 hesitant fuzzy sets (DT-2HFSs). CDT-2HFS is a proficient technique to cope with unpredictable and awkward information in realistic decision problems. CDT-2HFS is composed of the grade of truth and the grade of falsity, and the grade of truth (also for grade of falsity) contains the grade of primary and secondary parts in the form of polar coordinates with the condition that the sum of the maximum of the real part (also for the imaginary part) of the primary grade (also for the secondary grade) cannot exceed the unit interval [0, 1]. The aims of this manuscript are to discover the novel approach of CDT-2HFS and its operational laws. These operational laws are also justified with the help of an example. Additionally, based on a novel CDT-2HFS, we explored the correlation coefficient (CC) and entropy measures (EMs), and their special cases are also discussed. TOPSIS method based on CDT-2HFS is also explored. Then, we applied our explored measures based on CDT-2HFSs in the environment of the TOPSIS method, medical diagnosis, pattern recognition, and clustering algorithm to cope with the awkward and complicated information in realistic decision issues. Finally, some numerical examples are given to examine the proficiency and validity of the explored measures. Comparative analysis, advantages, and graphical interpretation of the explored measures with some other existing measures are also discussed.

Clustering within the Framework of Hesitant Fuzzy Sets

2014 ◽  
Vol 668-669 ◽  
pp. 1143-1146
Author(s):  
Yi Zhi Wang ◽  
Ying Jun Zhang ◽  
Lan Dong
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Matrix Composition ◽  
Clustering Method ◽  
Hesitant Fuzzy Sets ◽  
Correlation Relation ◽  
Numerical Example ◽  
Clustering Problem ◽  
Fuzzy Environment ◽  
Relation Matrix

In this paper, we propose a variety of correlation coefficient measures for hesitant fuzzy sets (HFSs) and investigate their properties. Moreover, we utilize the concepts of correlation relation matrix, composition matrix and equivalent correlation relation matrix to deal with the clustering problem under hesitant fuzzy environment. Finally, a numerical example is utilized to validate the proposed correlation coefficient measures and the clustering method.

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