Pattern Recognition Based on an Improved Szmidt and Kacprzyk’s Correlation Coefficient in Pythagorean Fuzzy Environment

2020 ◽  
pp. 190-206
Author(s):  
Paul Augustine Ejegwa ◽  
Yuming Feng ◽  
Wei Zhang
Keyword(s):  
Pattern Recognition ◽  
Correlation Coefficient ◽  
Fuzzy Environment

scholarly journals Novel concepts of $ m $-polar spherical fuzzy sets and new correlation measures with application to pattern recognition and medical diagnosis

2021 ◽  
Vol 6 (10) ◽  
pp. 11346-11379
Author(s):  
Muhammad Riaz ◽  
◽  
Maryam Saba ◽  
Muhammad Abdullah Khokhar ◽  
Muhammad Aslam ◽  
...  
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Real Life ◽  
Hybrid Structure ◽  
Fuzzy Environment ◽  
Life Problems ◽  
Correlation Measures ◽  
Relationship Of

<abstract><p>In this paper, we introduce the notion of $ m $-polar spherical fuzzy set ($ m $-PSFS) which is a hybrid notion of $ m $-polar fuzzy set ($ m $-PFS) and spherical fuzzy set (SFS). The purpose of this hybrid structure is to express multipolar information in spherical fuzzy environment. An $ m $-PSFS is a new approach towards computational intelligence and multi-criteria decision-making (MCDM) problems. We introduce the novel concepts of correlation measures and weighted correlation measures of $ m $-PSFSs based on statistical notions of covariances and variances. Correlation measures estimate the linear relationship of the two quantitative objects. A correlation may be positive or negative depending on the direction of the relation between two objects and its value lies the interval $ [-1, 1] $. The same concept is carried out towards $ m $-polar spherical fuzzy ($ m $-PSF) information. We investigate certain properties of covariances and the correlation measures to analyze that these concepts are extension of crisp correlation measures. The main advantage of proposed correlation measures is that these notions deal with uncertainty in the real-life problems efficiently with the help of $ m $-PSF information. We discuss applications of $ m $-polar spherical fuzzy sets and their correlation measures in pattern recognition and medical diagnosis. To discuss the superiority and efficiency of proposed correlation measures, we give a comparison analysis of proposed concepts with some existing concepts.</p></abstract>

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.

Novel Correlation Coefficient for Intuitionistic Fuzzy Sets and Its Application to Multi-Criteria Decision-Making Problems

2021 ◽  
Vol 10 (2) ◽  
pp. 39-58
Author(s):  
Ejegwa Paul Augustine
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Generalized Correlation

Correlation coefficient is an essential measuring operator in an intuitionistic fuzzy environment use in solving MCDM problems. In this paper, Xu et al.'s correlation coefficient for IFSs is generalized for an improved output. The objectives of this work are to generalize the triparametric correlation coefficient for IFSs proposed by Xu et al. and unravel its applicability in some MCDM problems. The generalized correlation coefficient for IFSs is characterized with some number of results. Some numerical illustrations are supplied to validate the preeminence of the generalized correlation coefficient for IFSs over some existing correlation coefficient measures. In addition, some MCDM problems such as determination of suitable lecturer for course allocation and personnel promotion exercise captured in intuitionistic fuzzy pairs are discussed with the aid of the proposed correlation coefficient.

scholarly journals Research on Novel Correlation Coefficient of Neutrosophic Cubic Sets and Its Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huiling Xue ◽  
Minrong Yu ◽  
Chunfang Chen
Keyword(s):  
Pattern Recognition ◽  
Comparative Analysis ◽  
Correlation Coefficient ◽  
Good Tool ◽  
Decision Method

Single-valued neutrosophic cubic set is a good tool to solve the vague and uncertain problems because it contains more information. The article first gives the correlation coefficient of single-valued neutrosophic cubic sets. Then, a decision method is proposed, and an application in pattern recognition is considered. Finally, examples are given to explain the feasibility of this method. At the same time, the comparative analysis shows the superiority of this method.

Intuitionistic Fuzzy Measures of Correlation Coefficient of Intuitionistic Fuzzy Numbers Under Weakest Triangular Norm

2019 ◽  
Vol 8 (1) ◽  
pp. 48-64 ◽  
Author(s):  
Mohit Kumar
Keyword(s):  
Correlation Coefficient ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Triangular Norm ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Technology Level

The correlation coefficient of variables has wide applications in statistics and is often calculated in crisp or fuzzy environment. This article extends the application of correlation coefficient to intuitionistic fuzzy environment. In this article, a new method is proposed to measure the correlation coefficient of intuitionistic fuzzy numbers using weakest triangular norm based intuitionistic fuzzy arithmetic operations. Different from previous studies, the correlation coefficient computed in this article is an intuitionistic fuzzy number rather than a crisp or fuzzy number. It is well known that the weakest t-norm arithmetic operations effectively reduce fuzzy spreads (fuzzy intervals) and provide more exact results. Therefore, a simplified, effective and exact method based on weakest t-norm arithmetic operations is presented to compute the correlation coefficient of intuitionistic fuzzy numbers. To illustrate the proposed method, the correlation coefficient between the technology level and management achievement from a sample of 15 machinery firms in Taiwan is calculated using proposed approach.

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