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.
Citation: Muhammad Riaz, Maryam Saba, Muhammad Abdullah Khokhar, Muhammad Aslam. Novel concepts of $ m $-polar spherical fuzzy sets and new correlation measures with application to pattern recognition and medical diagnosis[J]. AIMS Mathematics, 2021, 6(10): 11346-11379. doi: 10.3934/math.2021659
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.
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Muhammad Riaz, Maryam Saba, Muhammad Abdullah Khokhar, Muhammad Aslam. Novel concepts of $ m $-polar spherical fuzzy sets and new correlation measures with application to pattern recognition and medical diagnosis[J]. AIMS Mathematics, 2021, 6(10): 11346-11379. doi: 10.3934/math.2021659
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