An approach for finding fuzzy optimal and approximate fuzzy optimal solution of fully fuzzy linear programming problems with mixed constraints

Kumar and Kaur [A. Kumar and J. Kaur Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function. Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 26(1)(2014), 337-344.] proposed a method to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems with mixed constraints. They claimed that the FFLP problem with mixed constraints in which decision variables are represented by nonnegative triangular fuzzy numbers and the remaining parameters are represented by any type of triangular fuzzy numbers cannot be solved by any of the existing methods while all such FFLP problems can be solved by using their proposed method. In this paper, it is showed that the infeasibility case of the FFLP cannot be handled by the Kumar and Kaur's method. We have provided an extension to the method of Kumar and Kaur [A. Kumar and J. Kaur Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function. Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 26(1)(2014), 337-344.] to find fuzzy optimal solution to the feasible case and approximate fuzzy optimal solution to the infeasible case of FFLP problem with mixed constraints. To the best of our knowledge, there does not exist any study which deals with the infeasibility case of FFLP problem.