Generalization of discounted multistage decision making and control through fuzzy linguistic quantifiers: an attempt to introduce commonsense knowledge

A new class of models has been developed that make it possible to find an optimal sequence of controls best satisfying (fuzzy) constraints and goals at, say, most (or any other suitable linguistic quantifier) of the control stages.

Abstract

ABSTRACT This paper is an extension of work published by Kacprzyk in 1983 in which, by using a fuzzy-logic-based calculus of linguistically quantified propositions, some generalizations of multistage decision making and control have been proposed. Namely, a new class of models has been developed that make it possible, roughly speaking, to find an optimal sequence of controls best satisfying (fuzzy) constraints and goals at, say, most (or any other suitable linguistic quantifier, for example ‘almost all’, ‘at least a few’) of the control stages. In this paper we further extend the above-mentioned approach by introducing discounting (a variable importance of particular control stages, in principle ‘the earlier the more important’). We propose a new model that can find an optimal sequence of controls best satisfying the (fuzzy) constraints and goals at, say, most of the earlier control stages. We employ a fuzzy-logic-based calculus of linguistically quantified propositions and develop a branch-and-bound algorithm for solving the problem. The approach may be viewed as an attempt to introduce commonsense knowledge, in its fuzzy-disposition-based representation due to Zadeh, into multistage decision making and control models.