Trapezoidal Intuitionistic Fuzzy Fractional Transportation Problem

Naturally decision makers try to maximize ratio of return/risk, return/cost, and time/cost of transportation problem under uncertain environment. In such cases fractional transportation problem (FTP) play perfect role in instead of ordinary transportation problem. Some limited methods for the solution of fractional transportation problem using exact or fuzzy parameters are available in literature, and existing methods cannot deal uncertain FTP properly having hesitation factors due to inexact information. Here, I introduce the concept of intuitionistic fuzzy expectation of trapezoidal intuitionistic fuzzy numbers, and some related theorems are presented. Further, I present the concept of trapezoidal intuitionistic fuzzy fractional transportation (TIFFTP) problem, and a methodology for the solution of TIFFTP problem based on expectation of trapezoidal intuitionistic fuzzy numbers. Finally, I illustrate the presented TIFFTP problem by using an example.