A Two-Fold Linear Programming Model with Fuzzy Data

Literature Review

The theory of fuzzy mathematical programming was first proposed by Tanaka et al. (1974) based on the fuzzy decision framework of Bellman and Zadeh (1970) to address the impreciseness and vagueness of the parameters in problems with fuzzy constraints and objective functions. Zimmermann (1978) introduced the first formulation of FLP. He constructed a crisp model of the problem and obtained its crisp results using an existing algorithm. He then used the crisp results and fuzzified the problem by considering subjective constants of admissible deviations for the goal and the constraints. Finally, he defined an equivalent crisp problem using an auxiliary variable that represented the maximization of the minimization of the deviations on the constraints. Zimmermann (1978, 1987) used Bellman and Zadeh’s (1970) interpretation that a fuzzy decision is a union of goals and constraints.