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

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 r...

Full description

Bibliographic Details
Main Authors: Tahir Mahmood, Zeeshan Ali, Harish Garg, Lemnaouar Zedam, Ronnason Chinram
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/2568391
id doaj-dad4962ce68e4f18945688098f44a55c
record_format Article
spelling doaj-dad4962ce68e4f18945688098f44a55c2021-03-22T00:03:22ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/2568391Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their ApplicationsTahir Mahmood0Zeeshan Ali1Harish Garg2Lemnaouar Zedam3Ronnason Chinram4Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsSchool of MathematicsLaboratory of Pure and Applied MathematicsAlgebra and Applications Research UnitThe 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.http://dx.doi.org/10.1155/2021/2568391
collection DOAJ
language English
format Article
sources DOAJ
author Tahir Mahmood
Zeeshan Ali
Harish Garg
Lemnaouar Zedam
Ronnason Chinram
spellingShingle Tahir Mahmood
Zeeshan Ali
Harish Garg
Lemnaouar Zedam
Ronnason Chinram
Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications
Journal of Mathematics
author_facet Tahir Mahmood
Zeeshan Ali
Harish Garg
Lemnaouar Zedam
Ronnason Chinram
author_sort Tahir Mahmood
title Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications
title_short Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications
title_full Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications
title_fullStr Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications
title_full_unstemmed Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications
title_sort correlation coefficient and entropy measures based on complex dual type-2 hesitant fuzzy sets and their applications
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description 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.
url http://dx.doi.org/10.1155/2021/2568391
work_keys_str_mv AT tahirmahmood correlationcoefficientandentropymeasuresbasedoncomplexdualtype2hesitantfuzzysetsandtheirapplications
AT zeeshanali correlationcoefficientandentropymeasuresbasedoncomplexdualtype2hesitantfuzzysetsandtheirapplications
AT harishgarg correlationcoefficientandentropymeasuresbasedoncomplexdualtype2hesitantfuzzysetsandtheirapplications
AT lemnaouarzedam correlationcoefficientandentropymeasuresbasedoncomplexdualtype2hesitantfuzzysetsandtheirapplications
AT ronnasonchinram correlationcoefficientandentropymeasuresbasedoncomplexdualtype2hesitantfuzzysetsandtheirapplications
_version_ 1714772820430422016