Hyper BZ-algebras and semihypergroups

Y. Du, Xiaohong Zhang
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Abstract

In this paper, we introduce the new concept of a hyper BZ-algebra which is a generalization of BZ-algebra and hyper BCI-algebra, and give some examples and basic properties. We discuss the relationships among hyper BZ-algebras, hyper BCC-algebras and hyper BCI-algebra. Moreover, we propose the concepts of anti-grouped hyper BZ-algebras and generalized anti-grouped hyper BZ-algebras, and prove that the following important results:(1) Every anti-grouped hyper BZ-algebra is an anti-grouped BZ-algebra;(2) Every generalized anti-grouped hyper BZ-algebra corresponds to a semihypergroup. Finally, we present a method to construct a new hyper BZ-algebra by using a hyper BCC-algebra and a standard generalized anti-grouped hyper BZ-algebra.
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超bz代数与半超群
本文引入了超bz -代数的新概念,它是bz -代数和超bci -代数的推广,并给出了一些例子和基本性质。讨论了超bz -代数、超bcc -代数和超bci -代数之间的关系。此外,我们提出了反群超bz代数和广义反群超bz代数的概念,并证明了以下重要结果:(1)每个反群超bz代数都是一个反群的bz代数;(2)每个广义反群超bz代数对应一个半超群。最后,我们给出了一种利用超bcc -代数和标准广义反群超bz -代数构造一个新的超bz -代数的方法。
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Commutative ideals of BCI-algebras based on Łukasiewicz fuzzy sets Near Krasner hyperrings on nearness approximation space On the equivalence of sequences dependent on fuzzy ideals in the BCI-algebra Primary decomposition of A-ideals in MV-semimodules n-fold 2-nilpotent(solvable) ideal of a BCK-algebra
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