Modal operators on pseudo-BE algebras

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CIUNGU L.C.; BORUMAND SAEID A.; REZAEI A.

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Journal: Iranian Journal of Fuzzy Systems Year:2020 | Volume:17 | Issue:6 Page(s): 175-191

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Information Journal Paper

Title

Modal operators on pseudo-BE algebras

Author(s)

CIUNGU L.C. | BORUMAND SAEID A. | REZAEI A. | Issue Writer Certificate

Keywords

Non-classical logicQ2

pseudo-BE algebraQ2

modal operatorQ2

strong modal operatorQ2

modal deductive systemQ2

modal homomorphismQ2

Abstract

In this paper, we define and study the modal operators on pseudo-BE algebras as special cases of closure operators on these structures. We prove that the composition of two modal operators is a modal operator if and only if they commute. For the particular case of a good pseudo-BCK algebra an equivalent definition of the modal operators is given, and the notion of a strong modal operator is introduced and studied. We also define the notions of modal deductive systems and modal homomorphisms on pseudo-BE algebras and we investigate their properties. It is proved that, if two modal operators have the same image, then they coincide. Also, given a normal modal deductive system H of a distributive modal pseudo-BE algebra (A; f) we construct a modal operator on the quotient pseudo-BE algebra A=H.

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APA: Copy

CIUNGU, L.C., BORUMAND SAEID, A., & REZAEI, A.. (2020). Modal operators on pseudo-BE algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS, 17(6 ), 175-191. SID. https://sid.ir/paper/370086/en

Vancouver: Copy

CIUNGU L.C., BORUMAND SAEID A., REZAEI A.. Modal operators on pseudo-BE algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2020;17(6 ):175-191. Available from: https://sid.ir/paper/370086/en

IEEE: Copy

L.C. CIUNGU, A. BORUMAND SAEID, and A. REZAEI, “Modal operators on pseudo-BE algebras,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 17, no. 6 , pp. 175–191, 2020, [Online]. Available: https://sid.ir/paper/370086/en

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