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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

100%
Jun Y. B., Song S.-Z.
Bulletin of the Section of Logic
|
2020
|
tom 49
|
nr 1
EN
Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.
2
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Complex Fuzzy Sets with Application in BCK/BCI-Algebras

100%
Jun Y. B., Xin X. L.
Bulletin of the Section of Logic
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2019
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tom 48
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nr 3
173-185
EN
As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left (right) reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image (preimage) of a complex subalgebra and a complex left (right) reduced ideal.
3
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Int-Soft Ideals of Pseudo MV-Algebras

81%
Jun Y. B., Song S.-Z., Bordbar H.
Bulletin of the Section of Logic
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2018
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tom 47
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nr 1
EN
The notion of (implicative) int-soft ideal in a pseudo MV -algebra is introduced, and related properties are investigated. Conditions for a soft set to be an int-soft ideal are provided. Characterizations of (implicative) int-soft ideal are considered. The extension property for implicative int-soft ideal is established.
4
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Commutative Energetic Subsets of BCK-Algebras

81%
Jun Y. B., Roh E. H., Song S. Z.
Bulletin of the Section of Logic
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2016
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tom 45
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nr 1
EN
The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal.
5
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Positive Implicative Soju Ideals in BCK-Algebras

81%
Xin X. L., Borzooei R. A., Jun Y. B.
Bulletin of the Section of Logic
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2019
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tom 48
|
nr 1
EN
The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.
6
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Soju Filters in Hoop Algebras

81%
Borzooei R. A., Rezaei G. R., Kologhani M. A., Jun Y. B.
Bulletin of the Section of Logic
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2021
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tom 50
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nr 1
97-123
EN
The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.
7
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Length Neutrosophic Subalgebras of BCK=BCI-Algebras

81%
Jun Y. B., Khan M., Smarandache F., Song S.-Z.
Bulletin of the Section of Logic
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2020
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tom 49
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nr 4
377-400
EN
Given i, j, k ∈ {1,2,3,4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK=BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.
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On GE-algebras

81%
Bandaru R., Saeid A. B., Jun Y. B.
Bulletin of the Section of Logic
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2021
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tom 50
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nr 1
81-96
EN
Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.
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