An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

It presents the type-2 intuitionistic fuzzy solid transportation problem (type-2 IFSTP) in a real-world situation and introduces an efficient technique based on software codes for solving type-2 IFSTP. It defines various types of intuitionistic fuzzy solid transportation problems (IFSTPs) and presents a mathematical model of full and type-2 IFSTPs. Additionally, the theorem, corollary, and their proof, as well as some results relevant to type-2 IFSTPs, are presented. Both the existing problem’s solution and the proposed type-2 IFSTP’s solution are compared using software (e.g., Matlab). In particular, solving IFSTPs using Matlab is new in the literature. Shortcomings in the existing results are pointed out and solved. Using the proposed approach, the optimal solution and optimal objective value of both the solid transportation problem (STP) and type-2 IFSTPs are obtained concurrently with one LP model, which is the key objective of this article. It also discusses the time complexity of the existing algorithms for solving STPs with different intuitionistic fuzzy numbers (IFNs). Both the proposed results and the benefits of the proposed methodology are thoroughly discussed. Finally, a sound conclusion and future research directions are provided.