On Value-at-Risk and Conditional Value-at-Risk Measures for Intuitionistic and Picture Fuzzy Losses

Abstract

In this paper, we introduce alternative calculations of credibilistic Value-at-Risk (VaR) and Conditional VaR (CVaR) in intuitionistic and picture fuzzy (PF) environments, extending the findings of earlier research. Through the supposed dissolution of indeterminacy (or neutrality and refusal), a non-standard fuzzy number (FN) is transformed into a standard FN by computing its modified membership. This parameterized representative membership is a weighted average score function. Utilizing the existing credibility theory, these monetary measures can help manage non-standard fuzzy risk. Assuming the total cost as a loss function and using CVaR minimization models to identify the optimal values of the decision variables that result in minimal risk, we further apply the proposed approach to the intuitionistic fuzzy (IF) assignment problem and the PF transportation problem. Total costs are compared in order to perform error analyses and validation.