From computing with numbers to computing with words. From manipulation of measurements to manipulation of perceptions

Abstract

Discusses a methodology for reasoning and computing with perceptions rather than measurements. An outline of such a methodology-referred to as a computational theory of perceptions is presented in this paper. The computational theory of perceptions, or CTP for short, is based on the methodology of CW. In CTP, words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in a natural language. CW-based techniques are employed to translate propositions expressed in a natural language into what is called the Generalized Constraint Language (GCL). In this language, the meaning of a proposition is expressed as a generalized constraint, N is R, where N is the constrained variable, R is the constraining relation and isr is a variable copula in which r is a variable whose value defines the way in which R constrains S. Among the basic types of constraints are: possibilistic, veristic, probabilistic, random set, Pawlak set, fuzzy graph and usuality. The wide variety of constraints in GCL makes GCL a much more expressive language than the language of predicate logic. In CW, the initial and terminal data sets, IDS and TDS, are assumed to consist of propositions expressed in a natural language. These propositions are translated, respectively, into antecedent and consequent constraints. Consequent constraints are derived from antecedent constraints through the use of rules of constraint propagation. The principal constraint propagation rule is the generalized extension principle. The derived constraints are retranslated into a natural language, yielding the terminal data set (TDS). The rules of constraint propagation in CW coincide with the rules of inference in fuzzy logic. A basic problem in CW is that of explicitation of N, R, and r in a generalized constraint, X is R, which represents the meaning of a proposition, p, in a natural language.