Interval quantifying mapping of hedge algebras with adding special hedge.

Abstract

This paper introduces a new method of quantification of hedge algebras, which is different from the ordinary method by the fact that an artificial hedge h_0 should be added to model the context-dependent semantics of terms. It is aimed to represent the change of the semantics of any term x of length k appeared in the context X_{(k+1)} of terms with the length k + 1, so the meaning of a term will be changed when its adjacent terms are changed. Then, when x in the context X_{(k)} is presented in X_{(k+1)}, its semantics is represented by the expression h_0x. In this study, an enlarged hedge algebra AX^* of a given hedge algebra AX will be developed to model context-dependent semantics of terms of AX. New concepts of fuzziness measure, fuzziness intervals and interval quantifying mappings of terms are also introduced and examined. It is shown that trapezoidal fuzzy sets can be constructed to utilize a mathematical formalism.