Multi-objective interval type-2 fuzzy linear programming problem with vagueness in coefficient

Abstract

One of the most widely used fuzzy linear programming models is the multi-objective interval type-2 fuzzy linear programming (IT2FLP) model, which is of particular importance due to the simultaneous integration of multiple criteria and objectives in a single problem, the fuzzy nature of this type of problems, and thus, its closer similarity to real-world problems. So far, many studies have been done for the IT2FLP problem with uncertainties of the vagueness type. However, not enough studies have been done regarding the multi-objective interval type-2 fuzzy linear programming (MOIT2FLP) problem with uncertainties of the vagueness type. As an innovation, this study investigates the MOIT2FLP problem with vagueness-type uncertainties, which are represented by membership functions (MFs) in the problem. Depending on the localisation of vagueness in the problem, that is, vagueness in the objective function vector, vagueness in the technological coefficients, vagueness in the resources vector, and any possible combination of them, various problems may arise. Furthermore, to solve problems with MOIT2FLP, first, using the weighted sum method as an efficient and effective method, each of the MOIT2FLP problems is converted into a single-objective problem. In this research, these types of problems are introduced, their MFs are stated, and different solution methods are suggested. For each of the proposed methods, the authors have provided an example and presented the results in the corresponding tables.