Type 2 representation and reasoning for CWW

Abstract

Computing with words (CWW) is enriched by Type~2 fuzziness. Type~2 fuzziness exists and provides a richer knowledge representation and approximate reasoning for computing with words. First, it has been shown that membership functions, whether (1) they are obtained by subjective measurement experiments, such as direct or reverse rating procedures which captures varying degrees of membership and hence varying meanings of words or else (2) they are obtained with the application of modified fuzzy clustering methods, where they all reveal a scatter plot, which captures varying degrees of meaning for words in a fuzzy cluster. Secondly, it has been shown that the combination of linguistic values with linguistic operators, “AND”, “OR”, “IMP”, etc., as opposed to crisp connectives that are known as t-norms and t-conorms and standard negation, lead to the generation of Fuzzy Disjunctive and Conjunctive Canonical Forms, FDCF and FCCF, respectively. In this paper, we first discuss how one captures Type~2 representation. Then we concentrate on Type~2 reasoning that rests on Type~1 representation. Next, we show how one computes Type~2 reasoning starting with Type~2 representation. It is to be forecasted that in the new millennium more and more researchers will attempt to capture Type~2 representation and develop reasoning with Type~2 formulas that reveal the rich information content available in information granules, as well as expose the risk associated with the graded representation of words and computing with words. This will entail more realistic system model developments, which will help explore computing with perceptions, and computing with words by exposing graded flexibility as well as uncertainty embedded in meaning representation.