Fuzzy Programming Based on Interval-Valued Fuzzy Numbers and Ranking

In this paper, we use interval-valued fuzzy numbers to fuzzify the crisp linear programming to three cases. The first case, we use intervalvalued fuzzy numbers to fuzzify the coefficients in the objective function. We get a linear programming in the fuzzy sense. The second case, we use interval-valued fuzzy numbers to fuzzify the coefficients akj in the constraints about xj,j =1 , 2, ··· ,nand the constants bk,k =1 , 2, ··· ,m. We also get a linear programming in the fuzzy sense. The third case, we combine the first and the second cases.