Abstract—The purpose of this paper is to explain that a convex combination of several partial solutions using a new criterion which did not solve the fuzzy problem. The main feature of this paper is twofold. First, we prepare a simple optimization problem to explain the previously proposed approach that considered criteria separately. Consequently, we conclude, previous results are partial solutions. Secondly, we study the same optimization problem as the one that appears in a previously published paper. After his new criterion is added, we solve the new fuzzy optimization problem to demonstrate that the previous solution is not the optimal one. Hence, the previously proposed approach is questionable and then his assertion of the meaninglessness of the exact optimal solution for the fuzzy problem cannot be treated as a valid statement. At last, we cite a paper that had referred to the questionable approach which had been improved by another published article to support our argument.
Keywords—Fuzzy set, decision making, optimization, genetic algorithms, linear programming.
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