A New Goal Programming Approach for Multi-Objective Solid Transportation Problem with Interval-Valued Intuitionistic Fuzzy Logic

Abstract

Many researchers considered fuzzy and intuitionistic fuzzy parameters in the transportation problem, but we deal with interval-valued intuitionistic fuzzy parameters, which is another type of uncertainty that covers the favourable as well as unfavourable cases. In a multi-objective transportation problem, it is difficult to find the optimal solution for all objectives simultaneously. So, we have used the Intuitionistic Fuzzy Goal Programming (IFGP) with deviational function  (where  is fixed numerical weight for  which decided the importance of highest acceptance level of objective relative to other objectives) to find the compromise optimal solution. In this paper, we extend the model proposed by Nomani M.A. et al. in 2016 for Multi-Objective Solid Transportation Problem (MOSTP) with interval-valued intuitionistic fuzzy cost. We applied this approach to find the solution of the Solid Transportation Problem (STP) with satisfying all the constraints. To find the compromise optimal solution for all objectives simultaneously, we apply a new IFGP approach. The main focus of the proposed approach is to minimize the all objectives simultaneously and to obtain the solution nearly closed to the lower bounds of objectives. A numerical example is being carried out in favour of the proposed algorithm.