Modal operators on pseudo-BE algebras

Ciungu, L. C.; Borumand Saeid, A.; Rezaei, A.

doi:10.22111/ijfs.2020.5610

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	Modal operators on pseudo-BE algebras
Iranian Journal of Fuzzy Systems
دوره 17، شماره 6، بهمن و اسفند 2020، صفحه 175-191 اصل مقاله (437.78 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5610
نویسندگان
L. C. Ciungu^* ¹؛ A. Borumand Saeid²؛ A. Rezaei³
¹Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419, USA
²Department of Pure Mathematics, Faculty of Math. & Comput., Shahid Bahonar University of Kerman, Kerman, Iran
³Department of Mathematics, Payame Noor University, P.O.Box. 19395-3697, Tehran, Iran
چکیده
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.
کلیدواژه‌ها
Non-classical logic؛ pseudo-BE algebra؛ modal operator؛ strong modal operator؛ modal deductive system؛ modal homomorphism

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Modal operators on pseudo-BE algebras