Modality constrained programming problems: A unified approach to fuzzy mathematical programming problems in the setting of possibility theory

Abstract In this paper, fuzzy mathematical programming problems are formulated based on the idea analogous with the chance constrained programming problem. The difference in meaning between the ambiguity of the coefficients and that of the decision maker's preference is emphasized. The constraints with fuzzy coefficients are treated as the restriction that should be satisfied properly rather than perfectly. The objective functions with fuzzy coefficients are treated variously depending on the interpretations, i.e., the optimization of the modalities, the optimization of the fractile, the minimization of the ambiguity, and so forth. The deterministic equivalent constraints and the deterministic equivalent problems are shown when the constraints and the objective functions are linear. A numerical example is given to illustrate the proposed formulations.