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

  • Authors:

  • Nguyen Cat Ho

  • Affiliations:

  • Institute of Information Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet St., 10000 Hanoi, Vietnam

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

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.