The Expected Value Defuzzification Method for Pentagonal Fuzzy Number to Solve a Carbon Cost Integrated Solid Transportation Problem

The main feature of this paper is to propose the reduction method for the pentagonal fuzzy number using the expected value criterion. In this regard, some theoretical development is proposed for the pentagonal fuzzy number. As an application to the proposed reduction method, a single objective carbon cost integrated solid transportation problem minimizing the transportation cost along with the emission cost is solved with the parameters are as the pentagonal fuzzy number. To validate the proposed reduction method an analysis is outlined with the existing expected value reduction methods (viz. triangular and trapezoidal fuzzy numbers). After defuzzified the pentagonal fuzzy parameters, the equivalent deterministic problem is solved using the LINGO optimization solver. Based on the obtained solution, some important managerial decisions are finalized.