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.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

New distances for dual hesitant fuzzy sets and their application in clustering algorithm

2021 ◽  
pp. 1-12
Author(s):  
Yanxia Wei ◽  
Qinghai Wang
Keyword(s):  
Information System ◽  
Fuzzy Sets ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Membership Degree ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Important Data ◽  
Distance Measurements ◽  
Hybrid Distance

Compared to hesitant fuzzy sets and intuitionistic fuzzy sets, dual hesitant fuzzy sets can model problems in the real world more comprehensively. Dual hesitant fuzzy sets explicitly show a set of membership degrees and a set of non-membership degrees, which also imply a set of important data: hesitant degrees.The traditional definition of distance between dual hesitant fuzzy sets only considers membership degree and non-membership degree, but hesitant degree should also be taken into account. To this end, using these three important data sets (membership degree, non-membership degree and hesitant degree), we first propose a variety of new distance measurements (the generalized normalized distance, generalized normalized Hausdorff distance and generalized normalized hybrid distance) for dual hesitant fuzzy sets in this paper, based on which the corresponding similarity measurements can be obtained. In these distance definitions, membership degree, non-membership-degree and hesitant degree are of equal importance. Second, we propose a clustering algorithm by using these distances in dual hesitant fuzzy information system. Finally, a numerical example is used to illustrate the performance and effectiveness of the clustering algorithm. Accordingly, the results of clustering in dual hesitant fuzzy information system are compared using the distance measurements mentioned in the paper, which verifies the utility and advantage of our proposed distances. Our work provides a new way to improve the performance of clustering algorithms in dual hesitant fuzzy information systems.

scholarly journals Application of Dual Hesitant Fuzzy Geometric Bonferroni Mean Operators in Deciding an Energy Policy for the Society

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Raja Noshad Jamil ◽  
Tabasam Rashid
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Energy Policy ◽  
Multicriteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Multicriteria Decision ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Geometric Bonferroni Mean

Dual hesitant fuzzy geometric Bonferroni mean is defined for dual hesitant fuzzy sets. Different properties of dual hesitant fuzzy geometric Bonferroni mean are discussed. Some special cases are studied in detail for dual hesitant fuzzy geometric Bonferroni mean. In addition, dual hesitant fuzzy weighted geometric Bonferroni mean and dual hesitant fuzzy Choquet geometric Bonferroni mean are proposed. A multicriteria decision-making method is discussed to find the best alternative among different alternatives by using proposed aggregated operators and an illustrated example is also given to understand our proposal.

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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