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Journal articles on the topic '(implicative) falling neutrosophic ideal'

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Published: 4 June 2025

Last updated: 1 August 2025

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1

Takallo, M. Mohseni, Rajab Ali Borzooei, Seok-Zun Song, and Young Bae Jun. "Implicative ideals of BCK-algebras based on MBJ-neutrosophic sets." AIMS Mathematics 6, no. 10 (2021): 11029–45. http://dx.doi.org/10.3934/math.2021640.

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<abstract><p>The MBJ-neutrosophic set is applied to the implicative ideal of BCK-algebra to introduce the concept of implicative MBJ-neutrosophic ideal. Several properties are investigated. The relationship between implicative MBJ-neutrosophic ideal and each MBJ-neutrosophic subalgebra, (positive implicative, commutative) MBJ-neutrosophic ideal is established. Conditions for MBJ-neutrosophic subalgebra (resp., MBJ-neutrosophic ideal, positive implicative MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal) to be implicative MBJ-neutrosophic ideal are provided. Characteriz

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2

Muhiuddin, G., Seon Jeong Kim та Young Bae Jun. "Implicative 𝒩-ideals of BCK-algebras based on neutrosophic 𝒩-structures". Discrete Mathematics, Algorithms and Applications 11, № 01 (2019): 1950011. http://dx.doi.org/10.1142/s1793830919500113.

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In the present paper, we introduce the concept of neutrosophic implicative [Formula: see text]-ideal in [Formula: see text]-algebras, and investigate several properties. Also, we provide characterizations of the neutrosophic implicative [Formula: see text]-ideal. Furthermore, we discuss relations between neutrosophic positive implicative [Formula: see text]-ideal, neutrosophic commutative [Formula: see text]-ideal and neutrosophic implicative [Formula: see text]-ideal. Finally, we characterize implicative [Formula: see text]-algebra by using neutrosophic implicative [Formula: see text]-ideal.

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3

V., Amarendra Babu, Abida Begum K., and Siva Naga Malleswari V. "MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals." International Journal of Neutrosophic Science 21, no. 2 (2023): 84–97. http://dx.doi.org/10.54216/ijns.210208.

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The MBJ-Neutrosophic positive implicative LI-ideals, the MBJ-Neutrosophic associative LI-ideals, and the MBJ-Neutrosophic fantastic LI-ideals are all introduced in this study. Of all these ideals, several their qualities and corresponding conditions were explored. We have demonstrated how every positive implicative MBJ-Neutrosophic LI-ideal evolved into an MBJ-Neutrosophic LI-ideal, MBJ-Neutrosophic implicative LI-ideal, and MBJ-Neutrosophic fantastic LI-ideal. Additionally, it was demonstrated that any MBJ-Neutrosophic fantastic LI-ideal is a MBJ-Neutrosophic associative LI-ideal.

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4

Satyanarayana, B., Shake Baji, D. Ramesh, and Said Broumi. "Positive Implicative and Commutative BS-Neutrosophic Ideals of BCK/BCI-Algebra." International Journal of Neutrosophic Science 22, no. 2 (2023): 45–59. http://dx.doi.org/10.54216/ijns.220104.

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The notion of Positive Implicative BS-Neutrosophic Ideal, Commutative BS-Neutrosophic Ideal and related properties are investigated. Characterizations of Positive Implicative BS-Neutrosophic Ideal, Commutative BS- Neutrosophic Ideal are discussed.

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5

Jun, Young, Eun Roh, and Mehmet Öztürk. "Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows." Mathematics 6, no. 9 (2018): 149. http://dx.doi.org/10.3390/math6090149.

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The concepts of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are introduced, and several properties are investigated. Characterizations of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are obtained, and relations between a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and an intuitionistic fuzzy ideal are discussed. Conditions for an intuitionistic fuzzy ideal to be a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are provided, and relations between a positive implicative ( ∈ , ∈)-intu

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6

Jun, Young Bae, Seok-Zun Song, and Seon Jeong Kim. "Neutrosophic Quadruple BCI-Positive Implicative Ideals." Mathematics 7, no. 5 (2019): 385. http://dx.doi.org/10.3390/math7050385.

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By considering an entry (i.e., a number, an idea, an object, etc.) which is represented by a known part ( a ) and an unknown part ( b T , c I , d F ) where T , I , F have their usual neutrosophic logic meanings and a , b , c , d are real or complex numbers, Smarandache introduced the concept of neutrosophic quadruple numbers. Using the concept of neutrosophic quadruple numbers based on a set, Jun et al. constructed neutrosophic quadruple BCK/BCI-algebras and implicative neutrosophic quadruple BCK-algebras. The notion of a neutrosophic quadruple BCI-positive implicative ideal is introduced, and

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7

Yang, Yongwei, Xiaolong Xin, and Pengfei He. "Characterizations of MV-Algebras Based on the Theory of Falling Shadows." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/951796.

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Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of aT∧-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals andT-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be aT∧-fuzzy (implicative) ideal are provided. Some characterizations of falling fuzzy (implicative) ideals are presented by studying proprieties of them. The product⊛and the up product⊚operations on falling shadows and the upset of a falling shadow are estab

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8

Jun, Young Bae, Min Su Kang, and Chul Hwan Park. "Implicative Ideals of BCK-Algebras Based on the Fuzzy Sets and the Theory of Falling Shadows." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/819463.

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Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy implicative ideal of a BCK-algebra is introduced. Relations among falling fuzzy ideals, falling fuzzy implicative ideals, falling fuzzy positive implicative ideals, and falling fuzzy commutative ideals are given. Relations between fuzzy implicative ideals and falling fuzzy implicative ideals are provided.

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9

Alifviansyah, Kevin, and Agung Lukito. "BCK-Aljabar Kuadrupel Neutrosofik." MATHunesa: Jurnal Ilmiah Matematika 10, no. 1 (2022): 226–38. http://dx.doi.org/10.26740/mathunesa.v10n1.p226-238.

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Artikel ini memperkenalkan bilangan kuadrupel neutrosofik yang berbasis pada suatu himpunan untuk mengonstruksi BCK-aljabar kuadrupel neutrosofik. Kemudian diselidiki beberapa sifatnya dan akan dipelajari konsep ideal, ideal implikatif positif, ideal tertutup pada BCK-aljabar kuadrupel neutrosofik. Untuk subhimpunan dan dari BCK/BCI-aljabar kuadrupel neutrosofik, akan dikaji himpunan yang terdiri atas bilangan kuadrupel neutrosofik dengan syarat tertentu. Akan disajikan beberapa syarat agar himpunan menjadi ideal implikatif positif pada BCK-Aljabar kuadrupel neutrosofik dan himpunan menjadi id

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10

Borzooei, Rajab Ali, Young Bae Jun, M. Mohseni Takallo, and Sun Shin Ahn. "Positive Implicative Neutrosophic Quadruple BCK-Algebras and Ideals." New Mathematics and Natural Computation 17, no. 02 (2021): 403–23. http://dx.doi.org/10.1142/s1793005721500216.

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Given a set [Formula: see text], conditions for the neutrosophic quadruple [Formula: see text]-set to be a (positive implicative) neutrosophic quadruple [Formula: see text]-algebra are considered. The notion of (positive implicative) neutrosophic quadruple ideal is introduced, and the extended neutrosophic quadruple [Formula: see text]-algebra is established. Several properties are investigated.

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11

Muhiuddin, G., Ahmad Al-Kenani, Eun Roh, and Young Jun. "Implicative Neutrosophic Quadruple BCK-Algebras and Ideals." Symmetry 11, no. 2 (2019): 277. http://dx.doi.org/10.3390/sym11020277.

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A neutrosophic set is initiated by Smarandache, and it is a novel tool to deal with vagueness considering the truth, indeterminacy and falsity memberships satisfying the condition that their sum is less than 3. The concept of neutrosophic quadruple numbers was introduced by Florentin Smarandache. Using this idea, Jun et al. introduced the notion of neutrosophic quadruple B C K / B C I -numbers, and studied neutrosophic quadruple B C K / B C I -algebras. As a continuation of Jun et al.’s paper, the notion of implicative neutrosophic quadruple B C K -algebras is introduced, and several propertie

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12

Hashem, Bordba, Long Xin Xiao, Ali Borzooei Rajab, and Bae Jun Young. "Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows." February 11, 2022. https://doi.org/10.5281/zenodo.6041290.

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Neutrosophy is introduced by F. Smarandache in 1980 which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, or entity, ”A” in relation to its opposite, ”Anti-A” and that which is not A, ”Non-A”, and that which is neither ”A” nor ”Anti-A”, denoted by ”Neut-A”. Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. In this article,

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13

Xiao, Long Xin, Bordbar Hashem, Smarandache Florentin, Ali Borzooei Rajab, and Bae Jun Young. "Implicative falling neutrosophic ideals of BCK-algebras." February 18, 2021. https://doi.org/10.5281/zenodo.4549396.

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The notions of an implicative (∈, ∈)-neutrosophic ideal and an implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of an implicative (∈, ∈)-neutrosophic ideal are considered, and relations between an implicative (∈, ∈)-neutrosophic ideal and an (∈, ∈)-neutrosophic ideal are discussed. Conditions for an (∈, ∈)-neutrosophic ideal to be an implicative (∈, ∈)-neutrosophic ideal are provided, and relations between an implicative (∈, ∈)-neutrosophic ideal, a falling neu

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14

Rajab, Ali Borzooei, Mohseni Takallo M., Smarandache Florentin, and Bae Jun Young. "Positive implicative BMBJ-neutrosophic ideals in BCK-algebras." May 16, 2019. https://doi.org/10.5281/zenodo.2863127.

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The concepts of a positive implicative BMBJ-neutrosophic ideal is introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a (positive implicative) BMBJ-neutrosophic ideal are provided. Relations between BMBJ-neutrosophic ideal and positive implicative BMBJ-neutrosophic ideal are discussed. Characterizations of positive implicative BMBJ-neutrosophic ideal are displayed.

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15

Borzooei, Rajab Ali, M. Mohseni Takallo, Florentin Smarandache, and Young Bae Jun. "Positive implicative BMBJ-neutrosophic ideals in BCK-algebras." Neutrosophic Sets and Systems 23 (December 10, 2018). https://doi.org/10.5281/zenodo.2158371.

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The concepts of a positive implicative BMBJ-neutrosophic ideal is introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a (positive implicative) BMBJ-neutrosophic ideal are provided. Relations between BMBJ-neutrosophic ideal and positive implicative BMBJ-neutrosophic ideal are discussed. Characterizations of positive implicative BMBJ-neutrosophic ideal are displayed.

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16

Kul, Hur, Gon Lee Jeong, and Bae Jun Young. "Positive implicative MBJ-neutrosophic ideals of BCK/BCI-algebras." May 22, 2019. https://doi.org/10.5281/zenodo.3129296.

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The notion of positive implicative MBJ-neutrosophic ideal is introduced, and several properties are investigated. Relations between MBJ-neutrosophic ideal and positive implicative MBJ-neutrosophic ideal are discussed. Characterizations of positive implicative MBJ-neutrosophic ideal are displayed.

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17

Young, Bae Jun, Song Seok-Zun, Smarandache Florentin, and Bordbar Hashem. "Neutrosophic Quadruple BCK/BCI-Algebras." September 7, 2018. https://doi.org/10.5281/zenodo.1410851.

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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.

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18

Young, Bae Jun, Song Seok-Zun, Smarandache Florentin, and Bordbar Hashem. "Neutrosophic Quadruple BCK/BCI-Algebras." May 16, 2019. https://doi.org/10.5281/zenodo.2862227.

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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.

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19

Young, Bae Jun, Smarandache Florentin, and Ali Ozturk Mehmat. "Commutative falling neutrosophic ideals in BCK-algebras." April 28, 2018. https://doi.org/10.5281/zenodo.1235351.

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The notions of a commutative (∈, ∈)-neutrosophic ideal and a commutative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a commutative (∈, ∈)-neutrosophic ideal are obtained.

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