A New Correlation Coefficient for $T$-Spherical Fuzzy Sets and Its Application in Multicriteria Decision-Making and Pattern Recognition

Abstract

The goal of this paper is to design a new correlation coefficient for T -spherical fuzzy sets (TSFSs), which can accurately measure the nature of correlation (i.e., positive and negative) as well as the degree of relationship between TSFS. In order to formulate our proposed idea, we had taken inspiration from the statistical concept of the correlation coefficient. While doing so, we firstly introduce the variance and covariance of two TSFS and then constructed our scheme using these two newly defined notions. The numerical value of our proposed correlation coefficient lies within the interval − 1 , + 1 , as it should be from a statistical point of view, whereas the existing methods cannot measure the negative correlation between TSFS, as their numerical value falls within the interval 0 , 1 , which is not reasonable both statistically and intuitively. This aspect has also been thoroughly demonstrated using some numerical examples. The comparison results witnessed the dominance and upper hand of our proposed method over the existing definitions, with reliable and better results. In order to demonstrate the feasibility, usefulness, and practical application, we applied our proposed scheme to solve technical and scientific problems of multicriteria decision-making and pattern recognition. The numerical results show that our proposed scheme is practically suitable, technically applicable, and intuitively reasonable.

Multiple criteria decision analytic methods in management with T-spherical fuzzy information

“…T-SF sets are able to precisely explicate the decision-maker’s perceived opinions and assessments in an intellectual way when taking into account enhanced information space representation (Liu and Wang 2022 ; Park et al 2021 ). As a result, many researchers have given the T-SF hypothesis their undivided attention and produced worthwhile research findings (Ali et al 2022 ; Hussain et al 2022 ; Khan et al 2022 ; Xian et al 2022 ).…”

“…T-SF sets have drawn a lot of interest from academics because they boost the modeling capabilities for interpreting equivocal and imprecise information in sophisticated subjective judgment scenarios (Akram et al 2023 ; Özlü and Karaaslan 2022 ; Yang and Pang 2022 ). To assist decision-makers or analysts in multiple criteria assessment and decision analysis in challenging T-SF scenarios, numerous studies have created efficient and appealing methodologies (Ali et al 2022 ; Alothaim et al 2022 ; Hussain et al 2022 ; Zedam et al 2022 ).…”

“…T-SF sets can be deployed to cope with exceedingly uncertain information, enabling decision-makers (or analysts) to evaluate in a broader variety, with more flexibility, and to manage complex data (Ali et al 2022 ; Naseem et al 2022 ; Wang and Ullah 2022 ). T-SF sets are a beneficial tool for dealing with ambiguity and uncertainty when extra answers of the four forms, i.e., positivity, neutrality, negativity, and refusal, are sought in multiple-criteria assessment and selection issues (Chen 2022a ; 2022c ; Naz et al 2022 ).…”

“…Moreover, Guleria and Bajaj fully demonstrated the effectiveness of their evolutionary correlation coefficients through the agency of two application cases in pattern classification and clinical diagnosis. Ali et al ( 2022 ) proffered a helpful correlation coefficient in T-SF conditions to suitably determine the nature of positive and negative correlations as well as the extent of relationships between T-SF sets based on Guleria and Bajaj’s ( 2021 ) and Ullah et al’s ( 2020 ) suggested formulations of T-SF correlation coefficients. Additionally, to illustrate the suitability and utility of their idea, Ali et al used the recommended correlation coefficient to address the pattern recognition issues in the practical decision-making arena.…”

“…In other fuzzy circumstances related to T-SF sets, there was also the development of new types of correlation coefficients, such as new correlation coefficients in uncertain environments involving mixed SF and m-pole fuzziness (Riaz et al 2021 ), spherical fuzziness (Mahmood et al 2021 ), picture fuzziness (Singh and Ganie 2022 ), Pythagorean fuzziness (Li et al 2022 ), T-sphere type 2 hesitant fuzziness (Özlü and Karaaslan 2021). Given the excellent characteristics possessed by the T-SF correlation coefficients proposed by Ali et al ( 2022 ), Guleria and Bajaj ( 2021 ), Ullah et al ( 2020 ), and Wang and Chen ( 2022 ), the primary goal of this research is to utilize these enhanced correlation coefficients to illuminate T-SF correlation-oriented measurements for providing a strong foundation for the multiple criteria decision analytic methods, which constitutes the primary motivation for this research.…”