Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables

Abstract

Kumar et al. (Appl. Math. Model. 35:817-823, 2011) pointed out that there is no method in literature to find the exact fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. There may exist several FFLP problems with equality constraints in which no restriction can be applied on all or some of the fuzzy variables but due to the limitation of the existing method these types of problems can not be solved by using the existing method. In this paper a new method is proposed to find the exact fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy coefficients and unrestricted fuzzy variables. The proposed method can also be used to solve the FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. To show the advantage of the proposed method over existing method the results of some FFLP problems with equality constraints, obtained by using the existing and proposed method, are compared. Also, to show the application of proposed method a real life problem is solved by using the proposed method.

A new interactive approach for solving fully fuzzy mixed integer linear programming

“…It is pointed out by Kumar et al [12] that there is no method in literature to find the exact fuzzy optimal solution of FFLP problems and a new method is proposed to find the fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. To find the exact fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy coefficients and unrestricted fuzzy variables, a method is presented by Kaur and Kumar [13]. Also, their method is used to solve the FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients.…”

Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

“…Ahmad et al [19], Jayalakshmi and Pandian [20], Khan et al [21], Kumar et al [22], Lotfi et al [23], Najafi et al [24] and Nasseri et al [25] also studied the fully fuzzy linear programming problems based on triangular fuzzy numbers. Kaur and Kumar [26] studied the fully fuzzy linear programming problems based on trapezoidal fuzzy numbers. Baykasoglu and Gocken [27] used the particle swarm optimization method to solve the fuzzy mathematical programs with fuzzy decision variables in which only triangular fuzzy numbers were taken into account.…”

A MOLP Method for Solving Fully Fuzzy Linear Programming withLRFuzzy Parameters

“…The FLP problem is said to be a fully fuzzy linear programming (FFLP) problem if all the parameters and variables are considered as fuzzy numbers. In recent years, some researchers such as Lofti and Kumar were interested in the FFLP problems, and some solution methods have been obtained to the fully fuzzy systems [2][3][4] and the FFLP problems [5][6][7][8][9][10][11][12][13]. FFLP problems can be divided in two categories: (1) FFLP problems with inequality constraints; (2) FFLP problems with equality constraints.…”

“…Hosseinzadeh Lotfi et al [6] used the lexicography method to obtain the fuzzy approximate solutions of the FFLP problems. Allahviranloo et al [7] and Kumar et al [5,8] solved the FFLP problem by use of a ranking function.…”