Filter theory of BL algebras

DOI

書誌事項

公開日
2007-05-03
DOI
  • 10.1007/s00500-007-0178-7
公開者
Springer Science and Business Media LLC

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説明

In this paper we consider fundamental properties of some types of filters (Boolean, positive implicative, implicative and fantastic filters) of BL algebras defined in Haveshki et al. (Soft Comput 10:657–664, 2006) and Turunen (Arch Math Logic 40:467–473, 2001). It is proved in Haveshki et al. (2006) that if F is a maximal and (positive) implicative filter then it is a Boolean filter. In that paper there is an open problem Under what condition are Boolean filters positive implicative filters? One of our results gives an answer to the problem, that is, we need no more conditions. Moreover, we give simple characterizations of those filters by an identity form ∀ x, y(t(x, y) ∈ F), where t(x, y) is a term containing x, y.

収録刊行物

  • Soft Computing

    Soft Computing 12 419-423, 2007-05-03

    Springer Science and Business Media LLC

詳細情報 詳細情報について

  • CRID
    1871428068023938944
  • DOI
    10.1007/s00500-007-0178-7
  • ISSN
    14337479
    14327643
  • 本文言語コード
    en
  • データソース種別
    • OpenAIRE

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