×

A generalization of fuzzy multistage decision-making and control via linguistic quantifiers. (English) Zbl 0544.93004

This paper deals with some generalizations of control under fuzziness. Instead of seeking an optimal sequence of controls which best satisfies the fuzzy constraints and fuzzy goals at all control stages, here an optimal sequence is sought which satisfies them at most, much more than 50%, etc. The algebraic and substitution method of R. R. Yager [Fuzzy set theory, Proc. 2nd int. Semin., Linz/Austria 1980, 69-124 (1981; Zbl 0472.03019) and Int. J. Man-Mach. Stud. 19, 195-227 (1983; Zbl 0522.03013)] is used within a calculus of linguistically quantified statements.
In section 3, the conventional and the generalized approach for the formulation of control under fuzziness in linguistically quantified statements is given. Using the algebraic method, the control problem is solved for an arbitrary linguistic quantifier (section 4) when the class of quantifiers is confined to non-decreasing quantifiers, i.e. the more the fuzzy constraints and fuzzy goals are satisfied, the better. For the linear quantifier, the sequence of optimal controls is specified (Lemma 1, Prop. 1). The algebraic approach has the advantage of simplicity because the control problem may be solved by dynamic programming for a large class of linguistic quantifiers. However, for certain quantifiers the solution boils down to solving the same set of equations. This disadvantage is shown not to occur by using the substitution method (section 5). Examples for ’all’ and ’most’ are given. The optimal fuzzy decision is characterized for monotonic quantifiers (Prop. 2, 3), the solution algorithm is to find some path in a decision tree. Further properties of the decision-tree are discussed (section 5).
Reviewer: R.Fahrion

MSC:

93A10 General systems
90B50 Management decision making, including multiple objectives
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03B52 Fuzzy logic; logic of vagueness
68Q55 Semantics in the theory of computing
PDFBibTeX XMLCite
Full Text: DOI