Solution of Z-number-based multi-objective linear programming models with different membership functions

Abstract

In a universe full of fuzziness and uncertainty, it is an absolute blessing if some information is reliable to some degree. Considering the amount of uncertainty, Zadeh proposed the idea of Z-number, which carries both uncertainty and the reliability of the information. Uncertain information can be reliably conveyed using Z-numbers. On the other hand, one of the important and widely used decision-making techniques is linear programming. Currently, linear programming has been extensively explored using fuzzy information. Decisions made using linear programming with uncertain data are highly uncertain due to the lack of reliability of the information. An effective decision-making method is multi-objective linear programming (MOLP), in which the decision-maker attempts to draw conclusions from information containing conflicting attributes. In the MOLP problem, there may be different solution vectors corresponding to each objective function. One needs to find a compromise solution vector that satisfies each objective function to a certain extent based on the decision maker's suggested preferences. In this study, we use Z-number and MOLP to model the Z-number MOLP problem (ZMOLPP). Furthermore, we propose a strategy for solving ZMOLPP by transforming it into a crisp MOLP problem, and finally converting this crisp MOLP problem into a single-objective linear programming problem (LPP) using different shape functions. Additionally, we compare the results with existing MOLP problems in fuzzy settings to validate the proposed strategy.