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1.
Neutrosophic Quadruple BCK/BCI-Algebras
Hashem Bordbar, Young Bae Jun, Florentin Smarandache, Seok-zun Song, 2018, original scientific article

Abstract: The notion of a neutrosophic quadruple BCK/BCI number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B) , which consists of neutrosophic quadruple BCK/BCI-numbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. An example to show that the set {0˜} is not a positive implicative ideal in a neutrosophic quadruple BCK-algebra is provided, and conditions for the set {0˜} to be a positive implicative ideal in a neutrosophic quadruple BCK-algebra are then discussed.
Found in: osebi
Keywords: neutrosophic quadruple BCK/BCI-number, neutrosophic quadruple BCK/BCI-algebra, neutrosophic quadruple subalgebra, (positive implicative) neutrosophic quadruple ideal
Published: 01.12.2019; Views: 1812; Downloads: 0
.pdf Fulltext (284,81 KB)

2.
Fuzzy soft set theory with applications in hyper BCK-algebras
Hashem Bordbar, Mohammad Rahim Bordbar, Seok-zun Song, Young Bae Jun, 2020, original scientific article

Abstract: In the paper [P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 589–602], Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision-making problem. The aim of this paper is to apply a fuzzy soft set for dealing with several kinds of theories in hyper BCK-algebras. The notions of fuzzy soft hyper BCK-ideal, fuzzy soft weak hyper BCK-ideal, fuzzy soft s-weak hyper BCK-ideal, and fuzzy soft strong hyper BCK-ideal are introduced, and related properties and relations are investigated.
Found in: osebi
Keywords: fuzzy soft hyper BCK-ideal, fuzzy soft weak hyper BCK-ideal, fuzzy soft s-weak hyper BCK-ideal, fuzzy soft strong hyper BCK-ideal
Published: 24.02.2020; Views: 1729; Downloads: 0
.pdf Fulltext (108,62 KB)

3.
A new type of hesitant fuzzy subalgebras and ideals in BCK/BCI-algebras
Hashem Bordbar, Young Bae Jun, Seok Zun Song, 2017, original scientific article

Abstract: The concept of a hesitant union (
Found in: osebi
Keywords: Hesitant union, ∪-hesitant fuzzy subalgebra, ∪-hesitant fuzzy ideal
Published: 01.12.2019; Views: 1852; Downloads: 0
.pdf Fulltext (89,38 KB)

4.
Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation Maps
Hashem Bordbar, Young Bae Jun, Seok Zun Song, 2018, original scientific article

Abstract: Relations between I-quasi-valuation maps and ideals in BCK/BCI -algebras are investigated. Using the notion of an I-quasi-valuation map of a BCK/BCI-algebra, the quasi-metric space is induced, and several properties are investigated. Relations between the I-quasi-valuation map and the I-valuation map are considered, and conditions for an I-quasi-valuation map to be an I-valuation map are provided. A congruence relation is introduced by using the I-valuation map, and then the quotient structures are established and related properties are investigated. Isomorphic quotient BCK/BCI-algebras are discussed.
Found in: osebi
Keywords: ideal, I-quasi-valuation map, I-valuation map, quasi-metric
Published: 01.12.2019; Views: 1680; Downloads: 0
.pdf Fulltext (261,47 KB)

5.
INT-SOFT IDEALS OF PSEUDO M V -ALGEBRAS
Hashem Bordbar, Young Bae Jun, Seok Zun Song, 2018, original scientific article

Abstract: 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.
Found in: osebi
Keywords: int-soft ideal, implicative int-soft ideal.
Published: 02.12.2019; Views: 1603; Downloads: 0
.pdf Fulltext (166,77 KB)

6.
Tender and naive weak closure operations on lower BCK-semilattices.
Hashem Bordbar, 2018, original scientific article

Abstract: The notion of tender and naive weak closure operation is introduced, and their relations and properties are investigated. Using a weak closure operation "d" and an ideal A of a lower BCK-semilattice X with the greatest element 1, a new ideal K of X containing the ideal Acl of X is established. Using this ideal K, a new function clt : I(X) → I(X); A → K is given, and related properties are considered. We show that if "cl" is a tender (resp., naive) weak closure operation on I(X), then so are "clt" and clf.
Found in: osebi
Keywords: zeromeet element, meet ideal, relative annihilator, (finite type, tender, naive) weak closure operation.
Published: 02.12.2019; Views: 1675; Downloads: 0
.pdf Fulltext (648,16 KB)

7.
Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras
Hashem Bordbar, Young Bae Jun, Florentin Smarandache, Seok Zun Song, 2018, original scientific article

Abstract: The concept of a (∈, ∈)-neutrosophic ideal is introduced, and its characterizations are established. The notions of neutrosophic permeable values are introduced, and related properties are investigated. Conditions for the neutrosophic level sets to be energetic, right stable, and right vanished are discussed. Relations between neutrosophic permeable S- and I-values are considered.
Found in: osebi
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, neutrosophic (anti-)permeable S-value, neutrosophic (anti-)permeable I-value, S-energetic set, I-energetic set
Published: 02.12.2019; Views: 1682; Downloads: 0
.pdf Fulltext (297,13 KB)

8.
UNI-SOFT COMMUTATIVE IDEALS WITH THRESHOLDS IN BCK/BCI-ALGEBRAS
Hashem Bordbar, Seok Zun Song, Young Bae Jun, Kyoung Ja Lee, 2018, original scientific article

Abstract: The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a uni- soft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established.
Found in: osebi
Keywords: uni-soft ideal (with thresholds), uni-soft commutative ideal (with thresholds).
Published: 02.12.2019; Views: 1768; Downloads: 0
.pdf Fulltext (141,42 KB)

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