Genetic Algorithm Based Hybrid Approach to Solve Optimistic, Most-likely and Pessimistic Scenarios of Fuzzy Multi-objective Assignment Problem Using Exponential Membership Function

This paper discussed a genetic algorithm based hybrid approach to solve different scenario (optimistic scenario, most-likely scenario and pessimistic scenario) of fuzzy multi-objective assignment problem (FMOAP) using an exponential membership function in which coefficient of the objective function is described by triangular possibilities distribution (TDP). Moreover, we used the α-level sets to classify the fuzzy judgment for Decision maker (DM) to optimize different scenario of fuzzy objective functions. We used a fuzzy technique to solve multi-objective optimization problem in which DM is required to specify the indistinct aspiration level as per the his/her preference and genetic algorithm is used to solve the 0-1 optimization problem for different choices of shape parameter in the exponential membership function. A numerical example is provided to demonstrate the effectiveness of the proposed approach with data set form realistic situation.