A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges

The main aim of the investigation of hedge algebras is to discover an algebraic structure in the category of universal algebras of terms-domains of linguistic variables or to establish an algebraic approach to the semantic structure of terms-domains. The meaning of linguistic terms in general is vague, however vagueness is a concept which is difficult to be defined formally and reasonably. Motivated by introducing a mathematical foundation of qualitative and quantitative fuzziness of linguistic terms, this paper is aimed to introduce and investigate a completion of refined hedge algebras and obtain a class of complete ones. They will be defined by adding “limit” elements to refined hedge algebras in an axiomatization way. It is shown that a formal model of fuzziness of linguistic terms and hedges can be defined reasonably in this semantic structure and there is a closed relation between fuzziness of terms and semantic-based topology of these algebras.