A generalization of fuzzy multistage decision-making and control via linguistic quantifiers

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Abstract
Multistage incision-making (control) under fuzziness is considered. At each control stage, a fuzzy constraint is imposed on the control applied, and a fuzzy goal is imposed on the state attained. An optimal sequence of controls is sought which maximizes the membership function of the fuzzy decision which is assumed to be the intersection of fuzzy constraints and fuzzy goals. Thin is basically equivalent to the determination of an optimal sequence of controls which ‘ best satisfies the fuzzy constraints and fuzzy goals at nil the control stages ’. The generalization proposed in the paper replaces the strict ‘ all ’ the something milder, for example ‘ most ’: Thus, we seek an optimal sequence of controls which ‘ best satisfies the fuzzy constraints and fuzzy goals at, for example, most of the control stages ’. A calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used. First, the algebraic method is employed. The resulting control problem is solved by dynamic programming. Then, the substitution method is used and the resulting control problem reduces to finding some path in a decision tree.

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