Journal
FUZZY SETS AND SYSTEMS
Volume 158, Issue 4, Pages 436-451Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2006.09.013
Keywords
algebra; hedge algebra; fuzziness of terms; linguistic domain; semantically ordering relation; semantic-based topology
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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. (C) 2006 Elsevier B.V. All rights reserved.
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