A Comparative Study of Fuzzy Goal Programming And Chance Constrained Fuzzy Goal Programming

Abstract

This work is a comparative study of the traditional fuzzy goal programming model and the chance constrained fuzzy goal programming model. The right-hand side coefficient of the constraint matrix is assumed to be a right sided fuzzy number, and a random variable following the gumbel distribution, while the coefficients of the constraint matrix are triangular fuzzy numbers.The chance constrained problem is converted to its deterministic equivalence and the fuzzy constraints defuzzied. The bounds of the kth objectives are determined and utilized to obtain the membership function of the fuzzy goals. Lastly, the weighted sum goal programming technique is employed to obtain the optimal solution to the decision makers goal target using the attained membership function. Moreover, the CCFGP model proved a more satiscing approach to optimize the decision makers goals as it yielded an under-achievement of the decision makers goal target. Numerical illustration proved the superiority of the technique.