On pseudo-BCI-algebras
TL;DR: The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given in this article, where extensions of pseudo-PCI algebra are also considered.
Abstract: The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
Citations
More filters
TL;DR: A new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters, and the filter theory of basic implication algebras is established.
Abstract: The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.
32 citations
TL;DR: It is proved that, if a pseudo-BE(A) algebra A is commutative, then all deductive systems of A are commutatives, and it is shown that the kernel of a Bosbach state (state-morphism, measure, type II state operator, pseudo-valuation) is a Commutative deductive system.
8 citations
TL;DR: Some new properties of fuzzy associative filters, fuzzy p-filter, and fuzzy a-filter in pseudo-BCI algebras are investigated and it is proved that a fuzzy filter of a pseudo- BCI algebra is fuzzy a -filter if and only if it is both a fuzzy p -filter and a fuzzy q-filter.
Abstract: Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra is a fuzzy associative filter if and only if it is a fuzzy a-filter; (2) a filter (also known as pseudo-filter) of a pseudo-BCI algebra is associative if and only if it is an a-filter (also call it pseudo- filter); (3) a fuzzy filter of a pseudo-BCI algebra is fuzzy a-filter if and only if it is both a fuzzy p-filter and a fuzzy q-filter.
7 citations
Cites background or methods from "On pseudo-BCI-algebras"
...In 2008, as a generalization of 𝐵𝐶𝐼-algebra, Dudek and Jun [6] introduced the notion of pseudo-𝐵𝐶𝐼 algebra which is also generalization of pseudo-𝐵𝐶𝐾 algebra introduced by Georgescu and Iorgulescu in [7]....
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...[6] W. A. Dudek and Y. B. Jun, “Pseudo-BCI algebras,” East Asian Mathematical Journal, vol. 24, no. 2, pp. 187–190, 2008....
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...[14] Y. B. Jun and S. Z. Song, “Fuzzy pseudo-ideals of pseudo-BCK algebras,” Journal of Applied Mathematics and Computing, vol. 12, no. 1-2, pp. 243–250, 2003....
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...Note that the notion of pseudo-BCI algebra in this paper is indeed dual form of original definition in [6]; accordingly, the notion of pseudo-filter (or pseudo-BCI filter) is the dual form of pseudoideal (or pseudo-BCI ideal) in [9]....
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...[4] X. Ma, J. Zhan, and Y. B. Jun, “New types of fuzzy ideals of BCIalgebras,”Neural Computing and Applications, vol. 21, pp. 19–27, 2012....
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Posted Content•
TL;DR: In this article, the notions of neutrosophic hesitant fuzzy subalgebra and hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated.
Abstract: The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fuzzy subalgebras (filters) and hesitant fuzzy subalgebras (filters) is discussed. Five kinds of special sets are constructed by a neutrosophic hesitant fuzzy set, and the conditions for the two kinds of sets to be filters are given. Moreover, the conditions for two kinds of special neutrosophic hesitant fuzzy sets to be neutrosophic hesitant fuzzy filters are proved.
7 citations
References
More filters
Journal Article•
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TL;DR: In this article, the notion of pseudo-BCI algebras is introduced, and some properties are investigated Characterizations of pseudo BCI algesas are established Some conditions for a pseudo-PCI algebra to be a pseudoBCK algebra are given.
Abstract: As a generalization of BCI-algebras, the notion of pseudo-BCI algebras is introduced, and some of their properties are investigated Characterizations of pseudo-BCI algebras are established Some conditions for a pseudo-BCI algebra to be a pseudo-BCK algebra are given
50 citations
Journal Article•
TL;DR: It is shown that every pseudo-BCI homomorphic image and preimage of a pseudo- BCI ideal is also a pseudo -BCI ideal.
Abstract: The notions of pseudo-atoms, pseudo-BCI ideals and pseudo-BCI homomorphisms in pseudo-BCI algebras are introduced. Characterizations of a pseudo-BCI ideal are displayed, and conditions for a subset to be a pseudo-BCI ideal are given. The concept of a medial pseudo-BCI algebra is also introduced, and its characterization is provided. We show that every pseudo-BCI homomorphic image and preimage of a pseudo-BCI ideal is also a pseudo-BCI ideal.
45 citations
Proceedings Article•
01 Jan 201221 citations