fuzzy goal An iterative goal to solve bi-level fractional integer programming problem using fuzzy approach: bi level fraction integer - salah, aml salah (IJRDO-Journal of Applied Science, 2019)
This paper solves the bi-level integer linear fractional programming problems based on  fuzzy goal approach. At the first phase of the solution algorithm and to avoid the complexity of non-convexity of this problem, the authors finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-attainment variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem eﬃciently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure.