ROBUST OPTIMIZATION UNDER SOFTNESS IN A FUZZY LINEAR-PROGRAMMING PROBLEM

In this paper, we discuss the softness and the robustness of the optim ality in the setting of linear programming problems with a fuzzy objec tive function. A fuzzy goal defined on the deviation from the optimal value is introduced, in order to define the soft-optimal solution. Fuz zy coefficients are regarded as possibility distributions. A necessity measure based on the possibility distribution is used for defining a necessarily optimal solution, i.e., a robust-optimal solution. Since a necessarily optimal solution does not exist in many cases, a necessar ily soft-optimal solution is defined. A solution algorithm for the bes t necessarily soft-optimal solution is proposed. (C) 1998 Elsevier Sci ence Inc.