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Journal articles on the topic 'Neutrosophic BCI-algebras'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Agboola, A. A. A., and B. Davvaz. "Introduction to Neutrosophic BCI/BCK-Algebras." International Journal of Mathematics and Mathematical Sciences 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/370267.

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2

Muhiuddin, G. "p-ideals of BCI-algebras based on neutrosophic N -structures." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1097–105. http://dx.doi.org/10.3233/jifs-201309.

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In this paper, neutrosophic N -structures are applied to p-ideals of BCI-algebras. In fact, we introduce the notion of neutrosophic N -p-ideal in BCI-algebras, and investigate several properties. Further, we present characterizations of neutrosophic N -p-ideal. Moreover, we consider relations between a neutrosophic N -ideal and a neutrosophic N -p-ideal. Also, we provide conditions for a neutrosophic N -ideal to be a neutrosophic N -p-ideal. Furthermore, it is proved that the neutrosophic N -structure Q N G over Q is a neutrosophic N p -ideal of Q ⇔ G is a p-ideal of Q where G is a non-empty s

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3

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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4

Jun, Young Bae, and Eun Hwan Roh. "MBJ-neutrosophic ideals of BCK/BCI-algebras." Open Mathematics 17, no. 1 (2019): 588–601. http://dx.doi.org/10.1515/math-2019-0106.

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Abstract The notion of MBJ-neutrosophic ideal is introduced, and its properties are investigated. Conditions for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal are provided. In a BCK/BCI-algebra, a condition for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal is given. In a BCK-algebra, a condition for an MBJ-neutrosophic subalgebra to be an MBJ-neutrosophic ideal is given. In a BCI-algebra, conditions for an MBJ-neutrosophic ideal to be an MBJ-neutrosophic subalgebra are considered. In an (S)-BCK-algebra, we show that every MBJ-neutrosophic ideal is an MBJ-neutrosophic ∘-suba

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5

Jun, Young, Seok-Zun Song, Florentin Smarandache, and Hashem Bordbar. "Neutrosophic Quadruple BCK/BCI-Algebras." Axioms 7, no. 2 (2018): 41. http://dx.doi.org/10.3390/axioms7020041.

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6

Jaíyéọlá, Tèmítọ́pẹ́, Emmanuel Ilojide, Memudu Olatinwo, and Florentin Smarandache. "On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)." Symmetry 10, no. 10 (2018): 427. http://dx.doi.org/10.3390/sym10100427.

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In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be as

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7

G., Muhiuddin and Y. B. Jun. "p-semisimple neutrosophic quadruple BCI-algebras and neutrosophic quadruple p-ideals." Annals of Communications in Mathematics 1, no. 1 (2018): 26–37. https://doi.org/10.5281/zenodo.10041027.

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Characterizations of neutrosophic quadruple BCI-algebra are considered. Conditions for the neutrosophic quadruple BCI-set to be a p-semisimple BCI-algebra are provided. A condition for a subalgebra to be an ideal in neutrosophic quadruple BCIalgebra is given. Conditions for the set NQ(A, B) to be a neutrosophic quadruple closed ideal and neutrosophic quadruple p-ideal are discussed. Characterizations of neutrosophic quadruple p-ideal are considered. 

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8

Zhang, Xiaohong, Xiaoyan Mao, Yuntian Wu, and Xuehuan Zhai. "NEUTROSOPHIC FILTERS IN PSEUDO-BCI ALGEBRAS." International Journal for Uncertainty Quantification 8, no. 6 (2018): 511–26. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2018022057.

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9

Arsham Borumand Saeid and YoungBaeJun. "Neutrosophic subalgebras of $BCK/BCI$-algebras based on neutrosophic points." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 14, no. 1 (2017): 87–97. http://dx.doi.org/10.30948/afmi.2017.14.1.87.

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10

Jun, Young, Florentin Smarandache, and Hashem Bordbar. "Neutrosophic N-Structures Applied to BCK/BCI-Algebras." Information 8, no. 4 (2017): 128. http://dx.doi.org/10.3390/info8040128.

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11

Borzooei, Rajab Ali, Hee Sik Kim, Young Bae Jun, and Sun Shin Ahn. "MBJ-neutrosophic subalgebras and filters in $ BE $-algebras." AIMS Mathematics 7, no. 4 (2022): 6016–33. http://dx.doi.org/10.3934/math.2022335.

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<abstract><p>The concept of a neutrosophic set, which is a generalization of an intuitionistic fuzzy set and a para consistent set etc., was introduced by F. Smarandache. Since then, it has been studied in various applications. In considering a generalization of the neutrosophic set, Mohseni Takallo et al. used the interval valued fuzzy set as the indeterminate membership function because interval valued fuzzy set is a generalization of a fuzzy set, and introduced the notion of MBJ-neutrosophic sets, and then they applied it to BCK/BCI-algebras. The aim of this paper is to apply th

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12

Young Bae Jun. "Neutrosophic subalgebras of several types in $BCK/BCI$-algebras." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 14, no. 1 (2017): 75–86. http://dx.doi.org/10.30948/afmi.2017.14.1.75.

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13

Kul Hur, YoungBaeJun, and Jeonggon Lee. "Positive implicative MBJ-neutrosophic ideals of $BCK/BCI$-algebras." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 17, no. 1 (2019): 65–78. http://dx.doi.org/10.30948/afmi.2019.17.1.65.

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14

Shao, Songtao, Xiaohong Zhang, Chunxin Bo, and Florentin Smarandache. "Neutrosophic Hesitant Fuzzy Subalgebras and Filters in Pseudo-BCI Algebras." Symmetry 10, no. 5 (2018): 174. http://dx.doi.org/10.3390/sym10050174.

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15

YoungBaeJun, Hashem Bordbar, and Florentin Smarandache. "Neutrosophic falling shadows applied to subalgebras and ideals in $BCK/BCI$-algebras." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 15, no. 3 (2018): 253–63. http://dx.doi.org/10.30948/afmi.2018.15.3.253.

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16

Jun, Young, Florentin Smarandache, Seok-Zun Song, and Hashem Bordbar. "Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras." Mathematics 6, no. 5 (2018): 74. http://dx.doi.org/10.3390/math6050074.

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17

Takallo, M. Mohseni, R.A. Borzooei, and Young Bae Jun. "MBJ-neutrosophic structures and its applications in BCK/BCI-algebras." Neutrosophic Sets and Systems 23 (December 10, 2018). https://doi.org/10.5281/zenodo.2155212.

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Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be used as a mathematical tool for dealing with indeterminates and inconsistent information. As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced, and it is applied to BCK=BCI-algebras. The concept of MBJ-neutrosophic subalgebras in BCK=BCI-algebras is introduced, and related properties are investigated. A characterization of MBJ-neutrosophic subalgebra is pr

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18

Agboola, A.A.A., and B. Davvaz. "On Neutrosophic Ideals of Neutrosophic BCI-Algebras." July 1, 2015. https://doi.org/10.5281/zenodo.22614.

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The objective of this paper is to introduce and study neutrosophic ideals of neutrosophic BCI-algebras. Elementary properties of neutrosophic ideals of neutrosophic BCI-algebras are presented.

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19

Temitope, Gbolahan Jaiyéolá, Ilojide Emmanuel, Jamiu Saka Adisa, and Gabriel Ilori Kehinde. "On the Isotopy of some Varieties of Fenyves Quasi Neutrosophic Triplet Loop (Fenyves BCI-algebras)." February 5, 2020. https://doi.org/10.5281/zenodo.3640219.

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Neutrosophy theory has found application in health sciences in recent years. There is the need to develop neutrosophic algebraic systems which are good and appropriate for studying and understanding the effects of diseases and their possible treatments. In order to achieve this, special types of quasi neutrosophic loops and their isotopy needed to be introduced for this purpose. Fenyves BCI-algebras are BCI-algebras (special types of quasi neutrosophic loops) that satisfy the 60 Bol-Moufang identities. In this paper, the isotopy of BCI-algebras are studied. Neccessary and sufficient conditions

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20

Anas, Al-Masarwah, and Ghafur Ahmad Abd. "Structures on Doubt Neutrosophic Ideals of BCK/BCI-Algebras under (S, T)-Norms." May 3, 2020. https://doi.org/10.5281/zenodo.3783032.

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Smarandache implemented the idea of neutrosophic set theory as a method for dealing undetermined data. Neutrosophic set theory is commonly used in various algebric structures, such as groups, rings and BCK/BCI- algebras. At present, there exist no results on doubt neutrosophic ideals of BCK/BCI-algebras using t-conorm and t-norm. First, the notions of (S; T)- normed doubt neutrosophic subalgebras and ideals of BCK/BCI-algebras are introduced and the characteristic properties are described. Then, images and preimages of (S; T)- normed doubt neutrosophic ideals under homomorphism are considered.

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21

A., A. A. Agboola, and Davvaz B. "Introduction to Neutrosophic BCI/BCK-Algebras." November 3, 2015. https://doi.org/10.5281/zenodo.1041548.

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22

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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23

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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24

Seok-Zun, Song, Khan Madad, Smarandache Florentin, and Bae Jun Young. "A Novel Extension of Neutrosophic Sets and Its Application in BCK/BCI-Algebras." April 30, 2018. https://doi.org/10.5281/zenodo.1237866.

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Generalized neutrosophic set is introduced, and applied it to BCK/BCI-algebras. The notions of generalized neutrosophic subalgebras and generalized neutrosophic ideals in BCK/BCI-algebras are introduced, and related properties are investigated.

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25

Zhang, Xiaohong, Yingcang Ma, and Florentin Smarandache. "Neutrosophic Regular Filters and Fuzzy Regular Filters in Pseudo-BCI Algebras." October 14, 2017. https://doi.org/10.5281/zenodo.1012239.

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Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI algebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are discussed. Moreover, the relationships among neut

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26

A.A.A., Agboola, and Davvaz B. "Introduction to Neutrosophic BCI/BCK-Algebras." April 6, 2013. https://doi.org/10.5281/zenodo.23110.

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27

H., Bordbar, Mohseni Takallo M., Borzooei R.A., and Bae Jun Young. "BMBJ-neutrosophic subalgebra in BCI/BCK-algebras." February 5, 2020. https://doi.org/10.5281/zenodo.3638246.

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For the first time Smarandache introduced neutrosophic sets which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. the notion of BMBJ-neutrosophic set and subalgebra, as a generalization of a neutrosophic set, is introduced, and it’s application to BCI/BCK-algebras is investigated. The concept of BMBJ-neutrosophic subalgebras in BCI/BCK-algebras is introduced, and related properties are investigated. New BMBJ-neutrosophic subalgebra is established by using an BMBJ-neutrosophic subalgebra of a BCI/BCK-algebra. Alos, homomorphic (inverse) imag

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28

Xiaohong, Zhang, Mao Xiaoyan, Wu Yuntian, and Zhai Xuehuan. "NEUTROSOPHIC FILTERS IN PSEUDO-BCI ALGEBRAS." May 21, 2019. https://doi.org/10.5281/zenodo.3077461.

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The concept of the neutrosophic set was introduced by Smarandache; it is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. The notion of pseudo-BCI algebra was introduced by Dudek and Jun; it is a kind of nonclassical logic algebra and has a close connection with various noncommutative fuzzy logics. In this paper, neutrosophic set theory is applied to pseudo-BCI algebras. The new concepts of neutrosophic filter, neutrosophic normal filter, antigrouped neutrosophic filter, and neutrosophic p-filter in pseudo-BCI algebras are proposed, and their

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29

M., Mohseni Takallo, Bordbar Hashem, and Bae Jun Young. "BMBJ-neutrosophic ideals in BCK/BCI-algebras." July 9, 2019. https://doi.org/10.5281/zenodo.3275167.

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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.

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30

Temitope, Gbolahan Jaiyeola, Ilojide Emmanuel, Olaposi Olatinwo Memudu, and Smarandache Florentin. "On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)." May 16, 2019. https://doi.org/10.5281/zenodo.2862943.

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In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative.

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31

G., Muhiuddin, N. Al-Kenani Ahmad, Hwan Roh Eun, and Bae Jun Young. "Implicative Neutrosophic Quadruple BCK-Algebras and Ideals." May 20, 2019. https://doi.org/10.5281/zenodo.3044809.

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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 BCK/BCI-numbers, and studied neutrosophic quadruple BCK/BCI-algebras.

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32

G., Muhiuddin, Smarandache Florentin, and Bae Jun Young. "Neutrosophic quadruple ideals in neutrosophic quadruple BCI-algebras." April 6, 2019. https://doi.org/10.5281/zenodo.2631518.

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In the present paper, we discuss the Neutrosophic quadruple q-ideals and (regular) neutrosophic quadruple ideals and investigate their related properties. Also, for any two nonempty subsets U and V of a BCI-algebra S, conditions for the set NQ(U; V ) to be a (regular) neutrosophic quadruple ideal and a neutrosophic quadruple q-ideal of a neutrosophic quadruple BCI-algebra NQ(S) are discussed. Furthermore, we prove that let U; V; I and J be ideals of a BCI-algebra S such that I U and J V . If I and J are q-ideals of S, then the neutrosophic quadruple (U; V )-set NQ(U; V ) is a neutrosophic quad

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33

B., Satyanarayana, Baji Shake, and Bindu Madhavi U. "BS-Neutrosophic Structures in BCK/BCI-Algebras." October 3, 2023. https://doi.org/10.5281/zenodo.8404436.

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In this article we generalized a Smarandache’s neutrosophic set as BS-neutrosophic set and it is applied to BCK/BCI-algebras. The concept of BS-neutrosophic subalgebra, BS-neutrosophic ideal and related properties are investigated.

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34

Jun, Young Bae, Madad Khan, Florentin Smarandache, and Seok-Zun Song. "Length neutrosophic subalgebras of BCK/BCI-algebras." Bulletin of the Section of Logic, October 8, 2020. http://dx.doi.org/10.18778/0138-0680.2020.21.

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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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35

G., Muhiuddin, Smarandache Florentin, and Bae Jun Young. "Neutrosophic quadruple ideals in neutrosophic quadruple BCI-algebras." May 16, 2019. https://doi.org/10.5281/zenodo.2862271.

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36

Rajab, Ali Borzooei, Smarandache Florentin, and Bae Jun Young. "Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras." March 22, 2020. https://doi.org/10.5281/zenodo.3723613.

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k-polar generalized neutrosophic set is introduced, and it is applied to BCK/BCI-algebras. The notions of k-polar generalized subalgebra, k-polar generalized (2; 2 _q)-neutrosophic subalgebra and k-polar generalized (q; 2 _q)-neutrosophic subalgebra are defined, and several properties are investigated. Characterizations of k-polar generalized neutrosophic subalgebra and k-polar generalized (2; 2 _q)-neutrosophic subalgebra are discussed, and the necessity and possibility operator of k-polar generalized neutrosophic subalgebra are are considered. We show that the generaliged neutrosophic q-sets

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37

"p-semisimple neutrosophic quadruple BCI-algebras and neutrosophic quadruple p-ideals." Annals of Communications in Mathematics, 2018. http://dx.doi.org/10.62072/acm.2018.010103.

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Characterizations of neutrosophic quadruple BCI-algebra are considered. Conditions for the neutrosophic quadruple BCI-set to be a p-semisimple BCI-algebra are provided. A condition for a subalgebra to be an ideal in neutrosophic quadruple BCIalgebra is given. Conditions for the set NQ(A, B) to be a neutrosophic quadruple closed ideal and neutrosophic quadruple p-ideal are discussed. Characterizations of neutrosophic quadruple p-ideal are considered.

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38

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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39

G., Muhiuddin, Bordbar Hashem, Smarandache Florentin, and Bae Jun Young. "Further results on (∈,∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebras." April 28, 2018. https://doi.org/10.5281/zenodo.1235357.

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Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈,∈)-neutrosophic ideal. The relation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈,∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (&isi

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40

Seon, Jeong Kim, Song Seok-Zun, and Bae Jun Young. "Generalizations of Neutrosophic Subalgebras in BCK/BCI-Algebras Based on Neutrosophic Points." April 28, 2018. https://doi.org/10.5281/zenodo.1235361.

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Saeid and Jun introduced the notion of neutrosophic points, and studied neutrosophic subalgebras of several types in BCK/BCI-algebras by using the notion of neutrosophic points. More general form of neutrosophic points is considered in this paper, and generalizations of Saeid and Jun’s results are discussed.

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41

Songtao, Shao, Zhang Xiaohong, Bo Chunxin, and SMARANDACHE FLORENTIN. "Neutrosophic Hesitant Fuzzy Subalgebras and Filters in Pseudo-BCI Algebras." September 6, 2018. https://doi.org/10.5281/zenodo.1410343.

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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 fu

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42

A., Borumand Saeid \., and Bae Jun Young. "Neutrosophic subalgebras of BCK=BCI-algebras based on neutrosophic points." July 5, 2017. https://doi.org/10.5281/zenodo.1041633.

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The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set , intuitionistic fuzzy set (see [1]) and interval valued intuitionistic fuzzy set .

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43

Eunsuk, Yang, Hwan Roh Eun, and Bae Jun Young. "Ordered subalgebras of ordered BCI-algebras based on the MBJ-neutrosophic structure." January 19, 2024. https://doi.org/10.5281/zenodo.10531712.

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The neutrosophic set consists of three fuzzy sets called true membership function, false membership function and indeterminate membership function. MBJ-neutrosophic structure is a structure constructed using interval-valued fuzzy set instead of indeterminate membership function in the neutrosophicset. In general, the indeterminate part appears in a wide range. So instead of treating the indeterminate part as a single value, it is treated as an interval value, allowing a much more comprehensive processing. In an attempt to apply the MBJ-neutrosophic structure to ordered BCI-algebras, the notion

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Song, Khan, Smarandache, and Jun. "Interval neutrosophic sets applied to ideals in BCK/BCI-algebras." Neutrosophic Sets and Systems 18/2017 (February 18, 2018). https://doi.org/10.5281/zenodo.1175165.

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BCK-algebras entered into mathematics in 1966 through the work of Imai and Iseki, and have been applied to many branches of mathematics, such as group theory, functional analysis, probability theory and topology. In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.

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G., Muhiuddin, Bordbar Hashem, SMARANDACHE FLORENTIN, and Bae Jun Young. "Further results on neutrosophic subalgebras and ideals in BCK/BCI-algebras." September 6, 2018. https://doi.org/10.5281/zenodo.1410260.

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Neutrosophic set (NS) developed by Smarandache introduced neutrosophic set (NS) as a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.

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46

Bordbar, Hashem, Rajab Ali Borzooei, Florentin Smarandache, and Young Bae Jun. "A general model of neutrosophic ideals in BCK/BCI-algebras based on neutrosophic points." Bulletin of the Section of Logic, August 15, 2020. http://dx.doi.org/10.18778/0138-0680.2020.18.

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   More general form of (∈, ∈ ∨q)-neutrosophic ideal is introduced, and their properties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ))-neutrosophic ideal are discussed. Characterizations of (∈, ∈∨q(kT ,kI,kF ))-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an (∈, ∈∨q(kT ,kI ,kF ))-neutrosophic ideal are displayed.  

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Young, Bae Jun. "Neutrosophic subalgebras of several types in BCK=BCI-algebras." July 3, 2017. https://doi.org/10.5281/zenodo.1041635.

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Abstract:

The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.

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48

Eunsuk, Yang, Hwan Roh Eun, and Bae Jun Young. "Single valued neutrosophic ordered subalgebras of ordered BCI-algebras." November 30, 2023. https://doi.org/10.5281/zenodo.10224240.

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Young, Bae Jun, Smarandache Florentin, Song Seok-Zun, and Bordbar Hashem. "Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras." September 7, 2018. https://doi.org/10.5281/zenodo.1410847.

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The notion of neutrosophic set (NS) theory developed by Smarandache is a more general platform that extends the concepts of classic and fuzzy sets, intuitionistic fuzzy sets, and interval-valued (intuitionistic) fuzzy sets and that is applied to various parts: pattern recognition, medical diagnosis, decision-making problems, and so on .

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P., B. Remya, та Francina Shalini A. "On Neutrosophic Vague Binary 𝐁𝐙𝐌𝐕𝐝𝐌 Sub - algebra of 𝐁𝐙𝐌𝐕𝐝𝐌- algebra In Neutrosophic Vague Binary Sets". 12 грудня 2021. https://doi.org/10.5281/zenodo.5775141.

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In Model theory, common algebraic structures found are Lattices and Boolean Algebras. In the broad field of research, various algebraic structures can be introduced for a set. BCK, BCI, BCH, BH etc. are some of them. In this paper, a comparatively novel mixed structure namely, de Morgan BZMV – algebra, is presented for neutrosophic vague binary sets. Obviously, this is a mixed output pattern and more effective than the already existing single output approaches. Instead of our usual Boolean approach, this model is a kind of de Morgan lattice extension. Additionally, it takes the effects o

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