Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making

2019 ◽  
Vol 24 (3) ◽  
pp. 1647-1659 ◽  
Author(s):  
Kifayat Ullah ◽  
Harish Garg ◽  
Tahir Mahmood ◽  
Naeem Jan ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficients ◽  
Multi Attribute Decision Making

scholarly journals Modified Expression to Evaluate the Correlation Coefficient of Dual Hesitant Fuzzy Sets and Its Application to Multi-Attribute Decision Making

2021 ◽  
Author(s):  
Akanksha Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Real Life ◽  
Correlation Coefficients ◽  
Hesitant Fuzzy Set ◽  
Root Cause ◽  
Dual Hesitant Fuzzy Set ◽  
Multi Attribute Decision Making ◽  
Detailed Mathematical Analysis

The main objective of this paper is to understand all the existing correlation coefficients (CoCfs) to determine the relation and dependency between two variables of the fuzzy sets and its extensions for solving decision-making (DM) problems. To study the weighted CoCfs between two variables the environment chosen here is dual hesitant fuzzy set (DHFS) which is a generalization of a fuzzy set which considers the hesitant value of both the membership and non-membership elements of a set. Although there exists CoCfs for DHFS but a detailed mathematical analysis suggests that there exists some shortcomings in the existing CoCfs for DHFS. Thus, an attempt has been made to properly understand the root cause of the posed limitation in the weighted CoCfs for DHFS and hence, modified weighted CoCfs for DHFS has been proposed for solving DHFS multi-attribute decision making (MADM) problems i.e., DM problems in which rating value of each alternative over each criterion is represented by a DHFS in the real-life. Also, to validate the proposed expressions of weighted CoCfs for solving DHFS MADM problems, an existing real-life problem is evaluated and a systematic comparison of the solution is presented for clarification.

On Generalized Correlation Coefficients of Picture Fuzzy Sets With Their Applications

2021 ◽  
Vol 10 (2) ◽  
pp. 59-81
Author(s):  
Surender Singh ◽  
Abdul Haseeb Ganie ◽  
Sumita Lalotra
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Crucial Role ◽  
Correlation Coefficients ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Multi Attribute Decision Making ◽  
Picture Fuzzy Sets ◽  
Generalized Correlation

Picture fuzzy sets (PFSs) play a crucial role in uncertain/vague environments than intuitionistic fuzzy sets (IFSs) which do not take into consideration the degree of neutrality of an element. In this paper, the authors have proposed generalized correlation coefficients of PFSs along with some properties. The effectiveness and application of the proposed generalized correlation coefficients of PFSs in pattern recognition and multi-attribute decision making (MADM) is also discussed with the help of numerical examples.

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.

scholarly journals A Multi-Attribute Pearson’s Picture Fuzzy Correlation-Based Decision-Making Method

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 999 ◽  
Author(s):  
Jin ◽  
Wu ◽  
Sun ◽  
Zeng ◽  
Luo ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Ideal Point ◽  
New Correlation ◽  
Fuzzy Correlation ◽  
Relative Proximity ◽  
Fuzzy Madm ◽  
Multi Attribute Decision Making ◽  
Picture Fuzzy Sets

As a generalization of several fuzzy tools, picture fuzzy sets (PFSs) hold a special ability to perfectly portray inherent uncertain and vague decision preferences. The intention of this paper is to present a Pearson’s picture fuzzy correlation-based model for multi-attribute decision-making (MADM) analysis. To this end, we develop a new correlation coefficient for picture fuzzy sets, based on which a Pearson’s picture fuzzy closeness index is introduced to simultaneously calculate the relative proximity to the positive ideal point and the relative distance from the negative ideal point. On the basis of the presented concepts, a Pearson’s correlation-based model is further presented to address picture fuzzy MADM problems. Finally, an illustrative example is provided to examine the usefulness and feasibility of the proposed methodology.

Cubic Pythagorean fuzzy sets and their application to multi-attribute decision making with unknown weight information

2019 ◽  
Vol 37 (1) ◽  
pp. 1529-1544 ◽  
Author(s):  
Syed Zaheer Abbas ◽  
Muhammad Sajjad Ali Khan ◽  
Saleem Abdullah ◽  
Huafei Sun ◽  
Fawad Hussain
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Pythagorean Fuzzy Sets ◽  
Multi Attribute Decision Making
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