Solving Method for Linear Fractional Optimization Problem with Fuzzy Coefficients in the Objective Function

Abstract

The importance of linear fractional programming comes from the fact that many real life problems are based on the ratio of physical or economic values (for example cost/time, cost/volume, profit/cost or any other quantities that measure the efficiency of a system) expressed by linear functions. Usually, the coefficients used in mathematical models are subject to errors of measurement or vary with market conditions. Dealing with inaccuracy or uncertainty of the input data is made possible by means of the fuzzy set theory. Our purpose is to introduce a method of solving a linear fractional programming problem with uncertain coefficients in the objective function. We have applied recent concepts of fuzzy solution based on α-cuts and Pareto optimal solutions of a biobjective optimization problem. As far as solving methods are concerned, the linear fractional programming, as an extension of linear programming, is easy enough to be handled by means of linear programming but complicated enough to elude a simple analogy. We follow the construction of the fuzzy solution for the linear case introduced by Dempe and Ruziyeva (2012), avoid the inconvenience of the classic weighted sum method for determining Pareto optimal solutions and generate the set of solutions for a linear fractional program with fuzzy coefficients in the objective function.

Development of Unrestricted Fuzzy Linear Fractional Programming Problems Applied in Real Case

“…Then, we obtain the optimal solution as x 1 = 4.097, and x 2 = 3.064 And the optimal value of the problem as Z = 3.33. In Veeramani and Sumathi methods [51] the optimal values of the problems are By comparing the proposed method results with those of the existing method [51,58], based on Definition 2.7, we conclude that our method is more efficient than other existing methods.…”

“…In Figure 1, we compare the membership function for the proposed method and the existing methods [51,58]. Graph (Figure 1) shows that the modified technique yields better values of most of the membership functions and individual objective functions in comparison to the existing methods [51,58].…”

“…In Figure 1, we compare the membership function for the proposed method and the existing methods [51,58]. Graph (Figure 1) shows that the modified technique yields better values of most of the membership functions and individual objective functions in comparison to the existing methods [51,58]. It is clear that both the approaches are closer, but the modified methodology is efficient and requires less computation than earlier technique in terms of considering the solution preferences by the decision-maker at each level.…”

Solving Linear Fractional Programming Problem in symmetric trapezoidal fuzzy environment

“…The significance of fractional linear programming cames from the fact that many real-world problems are based on the ratio on financial, economic or physical values such as (cost/volume, profit /cost or cost/time) in production and financial planning [1]. Various application problems, can be derived as mathematical programming problems model, may be formulated with uncertainty.…”

Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs

“…Other application areas are for example resource allocation, pattern recogonization and machine learning. Recently fuzzy set covering problem have been studied by Saxena and Gupta [11,12], Stanojević and Stanojević [14], Huang et al [2], Sahraeian and Sdeq Kazemi [9], Shavandi and Mahlooji [13], Zimmermann [17], Li and Kwan [5,6]. They discussed various approaches for solving set covering problems.…”