Material implications in lattice effect algebras

In this paper we show that it is not acceptable using the minimal conditions of implication introduced for orthomodular lattices as minimal conditions of a good implication for lattice effect algebras. Hence, we first define the concept of a partial t-norm on bounded lattices. Then we obtain the con...

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Bibliographic Details
Published inInformation sciences Vol. 433-434; pp. 233 - 240
Main Authors Borzooei, R.A., Dvurečenskij, A., Sharafi, A.H.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2018
Subjects
Fuzzy implication
Lattice effect algebra
Partial t-norm
pt-Implication
Sasaki arrow
Partial t-norm
Lattice effect algebra
pt-Implication
Fuzzy implication
Sasaki arrow
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Summary:In this paper we show that it is not acceptable using the minimal conditions of implication introduced for orthomodular lattices as minimal conditions of a good implication for lattice effect algebras. Hence, we first define the concept of a partial t-norm on bounded lattices. Then we obtain the concept of a pt-implication on bounded involutive lattices by introducing some conditions using partial t-norms. Furthermore, we conclude that the Sasaki arrow which is a very important implication in lattice effect algebras is the best pt-implication on them. Finally, applying the Sasaki arrow, we construct a fuzzy implication on a lattice effect algebra and also we prove that it is a weak pt-implication as well.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2017.12.049