On credibilistic multi-objective linear programming problems with generalized intuitionistic fuzzy parameters

This paper first considers an approach based on credibilistic chance constraints and expected values for solving multiple objective linear programming problems (MOLPPs) involving generalized (intuitionistic) fuzzy coefficients and crisp decision variables. Chance constraints are used to manage the degree of confidence in meeting imprecise constraints. For the defuzzification of any objective function, the method employs its expected value. Finally, the weighted average of the resulting objectives is substituted in place of the objective function to obtain an equivalent crisp single-objective problem and a compromise solution. The secondary concern of this study is to provide a common strategy to generate both standard and non-standard generalized fuzzy numbers (FNs), especially generalized triangular types of FNs or intuitionistic FNs (IFNs). We consider IFNs to consist of two generalized FNs (GFNs), so we first focus on the simulation of GFNs. In the single-value simulation formulas for GFNs, we adopt two normalized approximations: the first preserves the expected interval, expected value, and fuzziness, while the second preserves the value and ambiguity. From this point of view, a new unified method to simulate GFNs is proposed for the error analysis of MOLPPs. Computational experiments are conducted to demonstrate the suggested methodology.

Automated summary

This paper proposes a method based on credibilistic chance constraints and expected values for solving multiple objective linear programming problems with generalized fuzzy coefficients and crisp decision variables. The method uses chance constraints to manage confidence in meeting imprecise constraints and employs expected values for defuzzification of objective functions. It also introduces a unified method for simulating generalized fuzzy numbers and conducts computational experiments to validate the proposed methodology.