A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems

Abstract

This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all the linear fractional programming models on the given set of constraints were solved separately. Next, all the linear fractional objective functions were linearized, membership functions of objective functions and decision variables controlled by decision-makers at the highest level calculated, and a fuzzy multi-objective linear programming model formed and solved as linear goal programming problem by using simplex algorithm. The efficiency of the proposed algorithm was investigated using an economic example, and the obtained results compared with those obtained using an existing method.

Solving multi level multi-objective linear programming (ML MOLP) problems with fuzzy parameters (FPs)

“…Table 1 shows the manufacturing data expressed in the form of triangular fuzzy numbers. Perić et al [19] solve a similar example but with data that are assumed to be fixed.…”

“…Dalman in [5] presents an interactive fuzzy methodology to solve two-level linear fractional programming problem with a single DM at the upper level and multiple DMs at the lower level. Perić et al in [18] propose a new fuzzy goal programming methodology to solve BL multi-objective linear programming problems with fixed parameters in objective functions and constraints while Perić et al in [20] present a methodology for solving ML MOLFP problems also with fixed parameters. Kaci and Radjef [12] developed a new method for solving the ML MOLP problem by first determining the set of all compromise solutions without taking into account the hierarchy of the problem, and then applying a simple criterion to test whether a given compromise solution is preferred or not.…”

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

“…Very recently, a number of papers have exhibited their interest to solve the FLFP problems [46][47][48][49][50][51]. Recently, several researchers had focused for solving linear programming by using multi-objective and transformation technique under fuzzy circumstances, see refer [52][53][54][55][56]. The main works and features of this paper are that we consider a new type of fuzzy arithmetic for triangular numbers in which the coefficients of the objective function and the constraints were represented by triangular fuzzy numbers with inequality constraints utilised in daily life problems.…”