Implementing Approximate X

The important idea of determining "Approximate X", in which X can be almost anything, was put forward by Lotfi Zadeh early last year. Implementing programs to realize this powerful concept involves abandoning some cherished ideas, and adopting some new ones. Zadeh\´s famous 1965 fuzzy set paper laid out the basis for Approximate X; the discrete fuzzy set, whose members are words. However, from the beginning there was a concentration on words that describe numbers; the concepts of linguistic variable and membership function defined on the real line obscured the more general case, in which the members of a discrete fuzzy set are words that can represent almost anything. The development of typical fuzzy control rules, with inescapable fuzzification of input numbers and defuzzification into output numbers, pushed non-numeric fuzzy sets further into the background. In this paper we take up in some detail the nature of programs designed to produce output in words rather than numbers: appropriate data types, inference methods, rule-firing patterns and definitions of possibility and necessity.