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Information Journal Paper

Title

COMMUTATIVE PSEUDO BE-ALGEBRAS

Pages

  131-144

Abstract

 The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties. We generalize some results proved by A. Walendziak for the case of commutative BE-algebras. We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-algebras also hold for commutative pseudo BE-algebras. For example, any finite commutative pseudo BE-algebra is a BE-algebra, and any commutative pseudo BE-algebra is a join-semilattice. Moreover, if a commutative pseudo BE-algebra is a meet-semilattice, then it is a distributive lattice. We define the pointed pseudo-BE algebras, and introduce and study the relative negations on pointed pseudo BE-algebras. Based on the relative negations we construct two closure operators on a pseudo BE-algebra. We also define relative involutive pseudo BE-algebras, we investigate their properties and prove equivalent conditions for a relative involutive pseudo BE-algebra. We define the relative Glivenko property for a relative good pseudo BE-algebra and show that any relative involutive pseudo BE-algebra has the relative Glivenko property.

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    APA: Copy

    CIUNGU, L.C.. (2016). COMMUTATIVE PSEUDO BE-ALGEBRAS. IRANIAN JOURNAL OF FUZZY SYSTEMS, 13(1), 131-144. SID. https://sid.ir/paper/686308/en

    Vancouver: Copy

    CIUNGU L.C.. COMMUTATIVE PSEUDO BE-ALGEBRAS. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2016;13(1):131-144. Available from: https://sid.ir/paper/686308/en

    IEEE: Copy

    L.C. CIUNGU, “COMMUTATIVE PSEUDO BE-ALGEBRAS,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 13, no. 1, pp. 131–144, 2016, [Online]. Available: https://sid.ir/paper/686308/en

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