Extended Transportation Models Based on Picture Fuzzy Sets

Abstract

Picture fuzzy set (PFS) is an extension of intuitionistic fuzzy set, and it is capable to analyze the transportation problems that contain uncertain and vague information. PFSs are applicable in situations where human decisions demand more variety of responses: yes, abstain, no, and rejection which cannot be addressed in the traditional FSs and IFSs. In this paper, we propose a technique to solve fully picture fuzzy transportation problems (FPFTPs) which are based on picture fuzzy linear programming formulation. Fully picture fuzzy transportation problems are developed by considering all the variables and parameters as nonnegative trapezoidal picture fuzzy numbers. A ranking function is used to transform picture fuzzy numbers into crisp numbers. A model is presented to explain the suggested scheme. Finally, comparison analysis of fully picture fuzzy transportation model with fully intuitionistic fuzzy transportation model and fully fuzzy transportation model is presented with pictorial illustrations.