Hesitant t-spherical fuzzy linear regression model based decision making approach using gradient descent method

Abstract

Hesitant fuzzy set based linear regression model is used to solve decision making problems, where each element is assessed with multiple membership grades. However, in order to handle uncertainty properly, non-membership and abstinence degrees of each elements are also considered as equally significant, which are not captured by hesitant fuzzy set. To resolve these limitations of hesitant fuzzy set based model, this paper proposes hesitant t-spherical fuzzy linear regression model, where hesitant t-spherical fuzzy set can efficiently handle both non-membership and abstinence degrees along with membership degree. The regression model is used to determine the imprecise functional relationship between the dependent and independent variables which are represented using hesitant t-spherical fuzzy set. We apply gradient descent technique to estimate the optimal coefficients of the variables used in the proposed regression model. Finally, the residuals of the regression are computed for the purpose of decision making. The proposed approach has been illustrated using three real life applications (robot selection, revenue generation, and material selection) and compared with the existing approaches. Moreover, we have used sensitivity analysis and weighted spearman’s rank correlation coefficient metrics to demonstrate that the outcome of the proposed model is more consistent and reliable to rank its best alternative compared to existing approaches, which shows its capability to solve real life uncertain decision-making problems.