Grey-fuzzy solution for multi-objective linear programming with interval coefficients

Purpose The purpose of this paper is to propose a method for solving multi-objective linear programming (MOLP) with interval coefficients using positioned programming and interactive fuzzy programming approaches. Design/methodology/approach In the proposed algorithm, first, lower and upper bounds of each objective function in its feasible region will be determined. Afterwards using fuzzy approach, considering a membership function for each objective function and finally using grey linear programming, the solution for this problem will be obtained. Findings According to the presented example, in this paper, the proposed method is both simple in use and suitable for solving different problems. In the numerical example mentioned in this paper, the proposed method provides an acceptable solution for such problems. Practical implications As in most real-world situations, the coefficients of decision models are not known and exact. In this paper, the authors consider the model of MOLP with interval data, since one of the solutions to cover uncertainty is using interval theory. Originality/value Based on using grey theory and interactive fuzzy programming approaches, an appropriate method has been presented for solving MOLP problems with interval coefficients. The proposed method, against the complex methods, has less effort and offers acceptable solutions.

INTERACTIVE FUZZY PROGRAMMING MODEL IN MULTI-OBJECTIVE INVENTORY CONTROL PROBLEM USING VARIOUS OPERATORS

This paper deals with the interactive fuzzy programming approach for Multi Objective Inventory Control Problem (MOICP). In multi-objective optimization problem, objectives are often non-commensurable and cannot be combined into a single objective. Moreover, the objectives usually conflict with each other in that any improvement of one objective can be achieved only at the expense of another. In real world, all objectives of MOICP are not rigid. Some are rigid and some are fuzzy or all are imprecise. Fuzzy goals are defined by different membership functions through interaction with decision maker. By making the aspiration levels more flexible and by assigning different values to the normal weights to corresponding objectives functions, different solutions are determined to interact with the decision maker.