Multi-objective programming approach for fuzzy linear programming problems

Abstract

A new method namely, level-sum method based on the multi-objective linear programming and the simplex method is proposed for computing an optimal fuzzy solution to a fuzzy linear programming problem inwhich fuzzy ranking functions are not used. The level-sum method is illustrated by numerical examples.

A note on multi-objective integer linear programming problems using pentagonal fuzzy numbers

“…Step 2 Find an efficient solution to the multi-objective integer linear programming problem obtained in step 1 using the sum of objectives method [3].…”

“…Allahviranloo et al [1] have introduced a new method by reducing the fuzzy integer linear programming models to crisp integer linear programming models. Pandian [3] solved fuzzy linear programming problems using multi-objective technique. Sahaya sudha et al [4] discussed multi-objective fuzzy linear programming problem with pentagonal fuzzy numbers.…”

Ranking Function Application for Optimal Solution of Fractional programming problem

“…Ranking functions are an interactive approach for solving fuzzy parameters together with many techniques [7,9,8,16,22]. They have proposed different methods for solving fuzzy linear programming problems are reduced to crisp linear programming problems and the resulted crisp linear programming problems is solved to obtain an optimal solution of the fuzzy linear programming problems [18,17,4,3,13,20]. Also, many researchers presented a ranking procedure fully fuzzy numbers with linear, multi objective programming problems function can be reduced to a crisp value problem to obtain the optimal solution [10,2,15].…”

Fully Fuzzy Multi-Level Linear Programming Problem

“…P. Pandian [8] introduced the level-sum method to compute an optimal fuzzy solution to FFLP problem which based on the multi-objective linear programming and the simplex method.…”