Article ID: | iaor19961305 |
Country: | Netherlands |
Volume: | 78 |
Issue: | 2 |
Start Page Number: | 231 |
End Page Number: | 241 |
Publication Date: | Mar 1996 |
Journal: | Fuzzy Sets and Systems |
Authors: | Sakawa Masatoshi, Inuiguchi Masahiro |
Keywords: | programming: linear, programming: multiple criteria |
In this paper, the concept of efficient solutions to the conventional multiobjective linear programming problems is extended to the fuzzy (possibilistic) coefficients case. Two kinds of efficient solution sets, i.e., a set of possible efficient solutions and a set of necessarily efficient solutions, are defined as fuzzy sets whose membership grades represent the possibility and necessity degrees to which the solution is efficient. A test to check the possible efficiency is discussed when a feasible solution is given. To do this, the authors first consider the interval case, where all fuzzy (possibilistic) coefficients degenerate into interval coefficients. In this case, a set of possibly efficient solutions degenerates into a usual (crisp) set. A necessary and sufficient condition of the possible efficiency for the interval case is presented. This condition shows that the possible efficiency is checked by solving a system of linear inequalities. Extending this result to the fuzzy (possibilistic) case, the degree of possibility efficiency is obtained by solving a nonlinear programming problem. The nonlinear programming problem is solved by the simplex and bisection methods.