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11.
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)

12.
UNI-SOFT IDEALS IN CORESIDUATED LATTICES
Hashem Bordbar, 2018, original scientific article

Abstract: The notion of the uni-soft idea is introduced, and related properties are investigated. Characterizations of the uni-soft ideal are discussed. The transfer of uni-soft ideal is considered, and relations between the uni-soft ideal and its transfer are investigated. Given a soft set, conditions for the transfer of soft set to be a uni-soft ideal.
Found in: osebi
Keywords: Coresiduated lattice, uni-soft ideal, transfer, support.
Published: 15.10.2020; Views: 1365; Downloads: 0
.pdf Fulltext (630,37 KB)

13.
BMBJ-neutrosophic ideals in BCK/BCI-algebras
Hashem Bordbar, Young Bae Jun, 2019, original scientific article

Abstract: The concepts of a BMBJ-neutrosophic ◦-subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are discussed. Relations between a BMBJ-neutrosophic subalgebra, a BMBJ-neutrosophic ◦-subalgebra and a (closed) BMBJ-neutrosophic ideal are considered.
Found in: osebi
Keywords: MBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic ideal, BMBJ-neutrosophic ◦-subalgebra.
Published: 02.12.2019; Views: 1909; Downloads: 0
.pdf Fulltext (223,15 KB)

14.
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: 1605; Downloads: 0
.pdf Fulltext (166,77 KB)

15.
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: 1678; Downloads: 0
.pdf Fulltext (648,16 KB)

16.
A Generalization of Semidetached Subalgebras in BCK∕BCI-algebras
Young Bae Jun, Mohammad Rahim Bordbar, Hashem Bordbar, 2019, original scientific article

Abstract: Generalization of the paper [Y. B. Jun and S. Z. Song, Semidetached subalgebras in BCK∕BCI-algebras, to appear in Bulletin of the Korean Mathematical Society] is discussed. Several conditions for a semidetached structure in BCK∕BCI-algebras to be a semidetached subalgebra are provided. The concepts of (∈¯,∈¯∨qk¯)-fuzzy subalgebra, k-left (k-right) (qk,∈∨qk)-fuzzy subalgebra, (qk¯,∈¯∨qk¯)-fuzzy subalgebra and (∈¯∨qk¯,∈¯∨qk¯)-fuzzy subalgebra are introduced, and relative relations and properties are discussed.
Found in: osebi
Keywords: ð2, 2_qkÞ-fuzzy subalgebra, k-left (k-right) ðqk, 2_qkÞ-fuzzy subalgebra, ð 2 _ qk, 2 _ qk Þ-fuzzy subalgebra, semidetached structure, semidetached subalgebra.
Published: 02.12.2019; Views: 1672; Downloads: 0
.pdf Fulltext (190,65 KB)

17.
Neutrosophic falling shadows applied to subalgebras and ideals in BCK/BCI-algebras
Hashem Bordbar, Florentin Smarandache, Young Bae Jun, 2018, original scientific article

Abstract: As a combination of neutrosophic set and falling shadow, neutrosophic falling shadow is introduced, and applied to BCK/BCI- algebras. Falling neutrosophic subalgebra and falling neutrosophic ideal in BCK/BCI-algebras are introduced, and related properties are investi- gated. Relations between falling neutrosophic subalgebra and falling neu- trosophic ideal are discussed. A characterization of falling neutrosophic ideal is established.
Found in: osebi
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, Neutro- sophic random set, Neutrosophic falling shadow, Falling neutrosophic subalgebra, Falling neutrosophic ideal.
Published: 02.12.2019; Views: 1601; Downloads: 0
.pdf Fulltext (324,41 KB)

18.
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: 1688; Downloads: 0
.pdf Fulltext (297,13 KB)

19.
IDEALS OF IS-ALGEBRAS BASED ON N-STRUCTURES
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2018, original scientific article

Abstract: The notion of a left (resp., right) NI-ideal is introduced, and related properties are investigated. Characterizations of a left (resp., right) NI-ideal are considered. Translations of a left (resp., right) NI-ideal are studied. We show that the homomorphic image (preimage) of a left (resp., right) NI-ideal is a left (resp., right) NI-ideal. The notion of retrenched left (resp., right) NI-ideals is introduced, and their properties are investigated.
Found in: osebi
Keywords: Left (resp., right) NI-ideal, translation, closed support, retrenched left (resp., right) NI-ideal.
Published: 02.12.2019; Views: 1622; Downloads: 0
.pdf Fulltext (118,91 KB)

20.
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: 1771; Downloads: 0
.pdf Fulltext (141,42 KB)

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