Modeling of a semantics core of linguistic terms based on an extension of hedge algebra semantics and its application

Computing with words and fuzzy linguistic rule based systems play important roles as they can find various significant applications based on simulating human capability. In fuzzy set approaches, words are mapped to fuzzy sets, on which work operations of the developed methodologies. The interpretability of the methodologies depends on how well word semantics is represented by fuzzy sets, which in practice are designed based on human-user's intuition. In these approaches there is no formal linkage of fuzzy sets with the inherent semantics of words to ensure the interpretability of fuzzy sets and, hence, fuzzy rules. Hedge algebras, as models of linguistic domains of variables, provide a formalism to generate triangular fuzzy sets of terms from their own semantics. This permits for the first time to design genetically terms along with their integrated triangular fuzzy sets and to construct effective fuzzy rule based classifiers. To answer the question if trapezoidal fuzzy sets can be used instead of triangular fuzzy sets in the above design method, in this study we introduce and develop the so-called enlarged hedge algebras, in which the concept of semantics core of words can be modeled. We show that these algebras provide a formal mechanism to design optimal words integrated with their trapezoidal fuzzy sets as well as fuzzy linguistic rule based classifiers to solve classification problems. Two case studies are examined to show the usefulness of the proposed algebras.