M. Inuiguchi et M. Sakawa, ROBUST OPTIMIZATION UNDER SOFTNESS IN A FUZZY LINEAR-PROGRAMMING PROBLEM, International journal of approximate reasoning, 18(1-2), 1998, pp. 21-34
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.