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.
Fully fuzzy linear programming Exact fuzzy optimal solution Trapezoidal fuzzy number
Lotfi FH, Allahviranloo T, Jondabeha MA, Alizadeh L (2009) Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Model 33:3151–3156