Modal operators on pseudo-BE algebras
Publish place: Iranian Journal of Fuzzy Systems، Vol: 17، Issue: 6
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-17-6_014
تاریخ نمایه سازی: 30 خرداد 1400
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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Authors
L. C. Ciungu
Department of Mathematics, University of Iowa, ۱۴ MacLean Hall, Iowa City, Iowa ۵۲۲۴۲-۱۴۱۹, USA
A. Borumand Saeid
Department of Pure Mathematics, Faculty of Math. & Comput., Shahid Bahonar University of Kerman, Kerman, Iran
A. Rezaei
Department of Mathematics, Payame Noor University, P.O.Box. ۱۹۳۹۵-۳۶۹۷, Tehran, Iran