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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
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| 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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آمار تعداد مشاهده مقاله: 237 تعداد دریافت فایل اصل مقاله: 284 |
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