A fuzzy interval weights approach in fuzzy goal programming for a multi-criteria problem

Goal Programming (GP) is an effective method to solve linear multi-objective problems.The weights play an important role for achieving the solution of the multi-objective programming problem according to the needs and desires of the decision makers (DMs), particularly in uncertain environments.To tackle such uncertain matter on the issue of weights, the proposed approach has taken the interval weights associated to the unwanted devotional variable in goal achievement function as triangular fuzzy numbers Hence, this study presents a new insight into interval weights to solve linear multi-objective fuzzy GP problems by introducing a defuzzification method based on the Data Envelopment Analysis (DEA) model to defuzzify groups of fuzzy interval weights.This method partitions these fuzzy numbers which cover all possible results in this interval, able to give us best and optimal weights. In the solution process, the interval weights which were derived from several pairwise interval judgment matrices associated with unwanted deviational variables are introduced to the goal achievement function with the objective of minimization of those deviations, and thus, realize the aspired goal levels of the problem. To illustrate the proposed approach, numerical examples are solved with the resulted real or crisp weights. An improved optimal solution is achieved when the interval weight is represented as fuzzy numbers with their middle points are geometric means as compared to normal interval weights associated with the maximum and minimum interval under same matrix for each standard GP model and fuzzy GP model