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Journal articles on the topic 'Neutrosophic ideals'

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Published: 2 June 2025
Last updated: 31 July 2025

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1

Saber, Yaser, Fahad Alsharari, and Florentin Smarandache. "On Single-Valued Neutrosophic Ideals in Šostak Sense." Symmetry 12, no. 2 (2020): 193. http://dx.doi.org/10.3390/sym12020193.

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Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak’s sense, which is considered as a generalization of fuzzy ideals in Šostak’s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, espe
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2

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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3

Satyanarayana, Bavanari, and Shake Baji. "Interval-Valued Neutrosophic N-d-ideal in d-algebra." Neutrosophic Optimization and Intelligent Systems 3 (July 25, 2024): 57–70. http://dx.doi.org/10.61356/j.nois.2024.3330.

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In this article we present the concept of interval-valued neutrosophic N-d-ideal by applying interval-valued neutrosophic N-structure to d-ideal of algebraic structure d-algebra. We proved that an interval-valued neutrosophic N-d-ideal's pre-image and image under homeomorphism and epimorphism, respectively, are also interval-valued neutrosophic N-d-ideals. We provided some characteristics of interval-valued neutrosophic N-d-ideal.
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4

admin, admin, P. Maragatha Meenakshi, Aiyared Iampan, and N. Rajesh. "Neutrosophic nil radicals of neutrosophic ideals in rings." International Journal of Neutrosophic Science 22, no. 4 (2023): 82–92. http://dx.doi.org/10.54216/ijns.220407.

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The notion of neutrosophic nil radicals of neutrosophic ideals in rings is introduced, and related properties are investigated. In addition, we study some relations between the nil radical of the neutrosophic polynomial ideal of the polynomial ring R[x] induced by a neutrosophic ideal of a ring R and the nil radical of a neutrosophic ideal of R. Finally, we find the result of neutrosophic nil radicals of neutrosophic ideals from the epimorphism of rings.
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5

Satyanarayana, Bavanari, Shake Baji та Anjaneyulu Naik K. "MBJ-Neutrosophic Structure Applied to BP-algebras: BP-subalgebras and α-ideals". Neutrosophic Systems with Applications 25, № 2 (2025): 80–88. https://doi.org/10.61356/j.nswa.2025.25471.

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In this article, we introduce the concepts of MBJ-neutrosophic BP-subalgebras and MBJ-neutrosophic α-ideals in BP-algebra by applying MBJ-neutrosophic logic to algebraic structure BP-algebra. We prove that the intersection of two MBJ-neutrosophic α-ideals and the inverse image of an MBJ-neutrosophic α-ideal are also MBJ-neutrosophic -ideals. Furthermore, we prove an MBJ-neutrosophic set is an MBJ-neutrosophic BP-subalgebra if and only if its level sets are BP-subalgebras.
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6

Hummdi, Ali Yahya, and Amr Elrawy. "On neutrosophic ideals and prime ideals in rings." AIMS Mathematics 9, no. 9 (2024): 24762–75. http://dx.doi.org/10.3934/math.20241205.

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<p>This article aims to introduce and explore the concept of neutrosophic ideals in the context of rings. Besides, we investigate how the property of regularity in a ring can be understood through the lens of neutrosophic ideals. We further present the concept of neutrosophic prime ideals and systematically identify all neutrosophic prime ideals in $ \mathbb{Z} $.</p>
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7

P. Agarwal, Ravi, Soheyb Milles, Brahim Ziane, Abdelaziz Mennouni, and Lemnaouar Zedam. "Ideals and Filters on Neutrosophic Topologies Generated by Neutrosophic Relations." Axioms 13, no. 5 (2024): 292. http://dx.doi.org/10.3390/axioms13050292.

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Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operati
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8

Al-Masarwah, Anas, M. Kaviyarasu, Kholood Alnefaie, and M. Rajeshwari. "Fermatean Neutrosophic INK-algebras." European Journal of Pure and Applied Mathematics 17, no. 2 (2024): 1113–28. http://dx.doi.org/10.29020/nybg.ejpam.v17i2.5090.

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This paper introduces the concept of the direct product of sets that involve Fermatean neutrosophic elements in structures called INK-algebras. It defines terms like the direct product of Fermatean neutrosophic INK-ideals in INK-algebras and Fermatean neutrosophic sets (FNSs), Fermatean neutrosophic INK-ideals (FNINK-Is), and Fermatean neutrosophic closed INK-ideals (FNCINK-Is). The proof of theorems illustrating the relationships between these ideas is included in the paper. It also defines the INK-sub algebra embedded in an INK-algebra and gives a theorem elucidating the connection between t
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9

M., Kaviyarasu, and Rajeshwari M. "Direct Product of Neutrosophic h-ideal in INK-Algebra." International Journal of Neutrosophic Science 20, no. 1 (2023): 119–27. http://dx.doi.org/10.54216/ijns.200110.

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In this paper, “we first define the belief of direct product from neutrosophic sets in INK algebras, neutrosophic set, neutrosophic h-ideals, neutrosophic INK-subalgebra and direct product of neutrosophic h-ideals in INK algebras. Let's prove some theorems that show that there is some connection between these principles. Finally, we define the INK subalgebra of the INK algebra and then offer the ideal theorem approximately the connection between its pix and the direct product from the neutrosophic h-ideals.
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10

Subha, V. S., and P. Dhanalakshmi. "Ideal theory of interval neutrosophic sets in subtraction algebras." Open Journal of Mathematical Sciences 6, no. 1 (2022): 262–68. http://dx.doi.org/10.30538/oms2022.0191.

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In this paper, we introduce the notion of interval neutrosophic ideals in subtraction algebras. Also, introduce the intersection and union of interval neutrosophic sets in subtraction algebras. We prove intersection of two-interval neutrosophic ideals is also an interval neutrosophic ideal. Some exciting properties and results based on such an ideal are discussed. Moreover, we define the homomorphism and homomorphism of interval neutrosophic sets. We prove the image of an interval neutrosophic subalgebra is also an interval neutrosophic sub-algebra.
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11

Aiyared, Aiyared, Pongpun Julatha, Rukchart Prasertpong, and Aiyared Iampan. "Neutrosophic sets in IUP-algebras: a new exploration." International Journal of Neutrosophic Science 25, no. 3 (2025): 540–60. http://dx.doi.org/10.54216/ijns.250343.

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The notions of neutrosophic IUP-subalgebras, neutrosophic IUP-ideals, neutrosophic IUP-filters, and neutrosophic strong IUP-ideals of IUP-algebras are introduced, and their basic properties are investigated. Conditions for neutrosophic sets to be neutrosophic IUP-subalgebras, neutrosophic IUP-ideals, neutrosophic IUPfilters, and neutrosophic strong IUP-ideals of IUP-algebras are provided. Relations between neutrosophic IUP-subalgebras (resp., neutrosophic IUP-ideals, neutrosophic IUP-filters, neutrosophic strong IUP-ideals) and their level subsets are considered.
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12

Songsaeng, Metawee, and Aiyared Iampan. "Neutrosophic Set Theory Applied to UP-Algebras." European Journal of Pure and Applied Mathematics 12, no. 4 (2019): 1382–409. http://dx.doi.org/10.29020/nybg.ejpam.v12i4.3543.

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The notions of neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strongly UP-ideals of UP-algebras are introduced, and several properties are investigated. Conditions for neutrosophic sets to be neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strongly UP-ideals of UP-algebras are provided. Relations between neutrosophic UP-subalgebras (resp., neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, neutrosophic strongly UP
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13

Vasu, M., and D. Ramesh Kumar. "NEUTROSOPHIC IDEALS OF NEUTROSOPHIC BCH-ALGEBRAS." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9719–25. http://dx.doi.org/10.37418/amsj.9.11.79.

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14

Alsharari, Fahad. "Single-Valued Neutrosophic Roughness via Ideals." International Journal of Analysis and Applications 22 (February 27, 2024): 38. http://dx.doi.org/10.28924/2291-8639-22-2024-38.

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In this paper, we connect the idea of single-valued neutrosophic ideal to the concept of single-valued neutrosophic approximation space to define the concept of single-valued neutrosophic ideal approximation spaces. We present the single-valued neutrosophic ideal approximation interior operator intψΦ and the single-valued neutrosophic ideal approximation closure operator clψΦ, and we present the single-valued neutrosophic ideal approximation preinterior operator pintψΦ and the single-valued neutrosophic ideal approximation pre-closure operator pclψΦ about this concerning single-valued neutroso
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15

Aiyared, Aiyared, N. Rajesh, and Aiyared Iampan. "Neutrosophic ideals of several types in UP (BCC)-algebras." International Journal of Neutrosophic Science 23, no. 3 (2024): 304–17. http://dx.doi.org/10.54216/ijns.230325.

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Characterizations of (∈,∈)-neutrosophic ideals and (q,∈ ∨q)-neutrosophic ideals are provided. Given special sets, so-called neutrosophic ∈-subsets, neutrosophic q-subsets, and neutrosophic (q,∈ ∨q)-subsets, conditions for the neutrosophic ∈-subsets, neutrosophic q-subsets, and neutrosophic (q,∈ ∨q)-subsets to be ideals are discussed.
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16

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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17

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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18

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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19

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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20

Granados, Carlos, and Suman Das. "Neutrosophic Q-Ideals of Neutrosophic Q-Algebra." Revista Facultad de Ciencias Básicas 17, no. 2 (2023): 91–99. http://dx.doi.org/10.18359/rfcb.5690.

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the study of neutrosophic sets in different fields has been growing in the last decade; it allows the modelling and studying of some physical, biological and behavioral phenomena. In this paper, we establish the notion of neutrosophic Q-ideal of neutrosophic Q-algebra, which is an extension of some results presented in fuzzy and intuitionistic fuzzy sets. Finally, we formulate severalconclusions.
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21

Borzooei, Rajab, Xiaohong Zhang, Florentin Smarandache, and Young Jun. "Commutative Generalized Neutrosophic Ideals in BCK-Algebras." Symmetry 10, no. 8 (2018): 350. http://dx.doi.org/10.3390/sym10080350.

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The concept of a commutative generalized neutrosophic ideal in a B C K -algebra is proposed, and related properties are proved. Characterizations of a commutative generalized neutrosophic ideal are considered. Also, some equivalence relations on the family of all commutative generalized neutrosophic ideals in B C K -algebras are introduced, and some properties are investigated.
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22

Iampan, Aiyared, and N. Rajesh. "Neutrosophic N-structures over Hilbert algebras." International Journal of Neutrosophic Science 23, no. 3 (2024): 208–19. http://dx.doi.org/10.54216/ijns.230318.

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The notions of neutrosophic N-subalgebras and neutrosophic N-ideals of Hilbert algebras are introduced, and several properties are investigated. Conditions for neutrosophic N-structures to be neutrosophic Nsubalgebras and neutrosophic N-ideals of Hilbert algebras are provided. The Cartesian product of neutrosophic N-structures is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic N-subalgebras and neutrosophic N-ideals.
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23

Satyanarayana, Bavanari, and Shake Baji. "A Study on the Polarity of Generalized Neutrosophic Ideals in BCK-Algebra." Neutrosophic Systems with Applications 22 (October 1, 2024): 31–42. http://dx.doi.org/10.61356/j.nswa.2024.22364.

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In this study, we apply k-polar generalized neutrosophic logic to the ideal of BCK-algebra and consequently introduce the notion of a k-polar generalized neutrosophic ideal in BCK-algebra with an example. We provide conditions for a k-polar generalized neutrosophic set to be a k-polar generalized neutrosophic ideal. We prove that every k-polar generalized neutrosophic ideal is a k-polar generalized neutrosophic subalgebra, but the converse is not true, which can be illustrated with an example. Furthermore, we prove that a k-polar generalized neutrosophic set is a k-polar generalized neutrosoph
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24

Iampan, Aiyared, S. Yamunadevi, P. Maragatha Meenakshi, and N. Rajesh. "A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets." International Journal of Neutrosophic Science 20, no. 4 (2023): 78–92. http://dx.doi.org/10.54216/ijns.200406.

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In this paper, we introduce the concepts of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals have also been studied. The relationshipbetween neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals is also supplied. Finally, we
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25

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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26

Mandal, Debabrata. "Neutrosophic Soft $\Gamma$-Semiring and Its Ideals." International Journal of Fuzzy System Applications 7, no. 2 (2018): 103–13. http://dx.doi.org/10.4018/ijfsa.2018040106.

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As a generalization of fuzzy sets, soft set and neutrosophic sets are applied to many branches of mathematics to overcome the complexities arising from uncertain data. Combining these notions, in this article, the author initiates the study of $\Gamma$-semirings, an extension of semirings, and its ideals by neutrosophic soft sets. After defining some necessary definitions, they investigate neutrosophic soft $\Gamma$-semiring, neutrosophic soft ideals, idealistic neutrosophic soft $\Gamma$-semiring and obtain some of its characterizations.
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27

Manivasan, S., and P. Kalidass. "MBJ-neutrosophic Ideals of KU-algebras." Journal of Physics: Conference Series 2070, no. 1 (2021): 012047. http://dx.doi.org/10.1088/1742-6596/2070/1/012047.

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Abstract In this paper, the notion of MBJ-neutrosophic ideal for KU-algebra is introduced and its properties are investigated. Also, a condition for an MBJ-neutrosophic subalgebra to be an MBJ-neutrosophic ideal and converse part of a KU-algebra are discussed.
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28

Kumaran, K. Lenin Muthu, and A. Rajalakshmi. "Anti-neutrosophic fuzzy ideals of near-rings." Journal of Interdisciplinary Mathematics 27, no. 5 (2024): 1199–215. http://dx.doi.org/10.47974/jim-1954.

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In this article, we characterize the anti-neutrosophic fuzzy ideals of near-rings with an example. Here we introduce notion of anti-neutrosophic fuzzy subnear-rings and how they related to ideals within the near-rings. Finally, we provide an example illustrating the application of anti -neutrosophic fuzzy ideals within the context of a specific near-ring.
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29

Malleswari, V. S. N., M. Babu Prasad, Kothuru Bhagya Lakshmi, M. Aruna kumari, and M. Sireesha. "MBJ-Neutrosophic WI Ideals in Lattice Wajsberg Algebra." International Journal of Neutrosophic Science 23, no. 3 (2024): 131–39. http://dx.doi.org/10.54216/ijns.230311.

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In this study, we introduce the concepts of MBJ-Neutrosophic WI-ideal and MBJ-Neutrosophic lattice ideal of lattice Wajsberg algebras. We demonstrate that every MBJ-Neutrosophic WI-ideal of lattice Wajsberg algebra is an MBJ-Neutrosophic lattice ideal of lattice Wajsberg algebra. Additionally, we talk about its opposite. Furthermore, we discover that in lattice H-Wajsberg algebra, every MBJ-Neutrosophic lattice ideal is an MBJ-Neutrosophic WI-ideal.
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30

Zhou, Xin, and Xiao Long Xin. "Ideals on neutrosophic extended triplet groups." AIMS Mathematics 7, no. 3 (2021): 4767–77. http://dx.doi.org/10.3934/math.2022264.

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<abstract><p>In this paper, we introduce the concept of (prime) ideals on neutrosophic extended triplet groups (NETGs) and investigate some related properties of them. Firstly, we give characterizations of ideals generated by some subsets, which lead to a construction of a NETG by endowing the set consisting of all ideals with a special multiplication. In addition, we show that the set consisting of all ideals is a distributive lattice. Finally, by introducing the topological structure on the set of all prime ideals on NETGs, we obtain the necessary and sufficient conditions for th
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31

Riad Alabdullah, Murhaf. "Some Special Refined Neutrosophic Ideals in Refined Neutrosophic Rings: A Proof-of-Concept Study." Neutrosophic Systems with Applications 13 (December 8, 2023): 32–44. http://dx.doi.org/10.61356/j.nswa.2024.96.

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In this research, we created notions of a refined neutrosophic prime (completely prime, semiprime, and completely semiprime) ideal in a refined neutrosophic ring. If R(I1, I2) is a refined neutrosophic ring, then each ideal of R(I1, I2) has the form J+KI1+LI2 are ideals of the classical ring R. The objective of this work is to find the necessary and sufficient condition on classical ideals J, L and K that makes J+KI1+LI2 a prime (completely prime, semiprime, and completely semiprime) ideal in R(I1, I2). We studied some of the elementary properties of these concepts and the most important prope
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32

Shawqi, Shawqi, and Adel Al Al-Odhari. "Characteristics Neutrosophic Ideals For Neutrosophic Rings: On Review." Prospects for Applied Mathematics and Data Analysis 4, no. 1 (2024): 01–13. https://doi.org/10.54216/pamda.040101.

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The main objective of this paper is to present a review study with more information on the neutrosophic Ideal, Principle Ideal, Prim Ideal, Pseudo Neutrosophic Ideal, Quotient ring, and Pseudo Quotient ring. Neutrosophic ring theory is a branch of neutrosophic Algebra which introduced by Florentin Smarandache in 2006.
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33

A., Arulselvam V. Chinnadurai and S.V. Manemaran. "Pythagorean Q-anti neutrosophic ideals in gamma semigroup." Annals of Communications in Mathematics 5, no. 2 (2022): 88–96. https://doi.org/10.5281/zenodo.10058200.

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In this article, we define the concept of Pythagorean Q-anti neutrosophic ideal in gamma semigroup, Pythagorean Q-anti neutrosophic bi-ideal in gamma semigroup, and Pythagorean Q-anti neutrosophic interior ideal in gamma semigroup. We have illustrated the definition with an example. We have shown that Pythagorean Q- anti neutrosophic bi-ideal is a fuzzy bi-ideal and Pythagorean Q-anti neutrosophic ideal is a Pythagorean Q-anti neutrosophic interior ideal. Also, we have established some of its properties in detail. 
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34

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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35

Florentin, Smarandache, Ali Mumtaz, Naz Munazza, and Shabir Muhammad. "SOFT NEUTROSOPHIC LEFT ALMOST SEMIGROUP." May 22, 2014. https://doi.org/10.5281/zenodo.49127.

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In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LA-semigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutrosophic ideals respectively. We have found some new notions related to the strong or pure part of neutrosophy and we give explaination with necessary illustrative examples. We have also given rigorious
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36

Florentin, Smarandache, Ali Mumtaz, Naz Munazza, and Shabir Muhammad. "Soft Neutrosophic Left Almost Semigroup." April 13, 2014. https://doi.org/10.5281/zenodo.30319.

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In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LAsemigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutrosophic ideals respectively. We have found some new notions related to the strong or pure part of neutrosophy and we give explaination with necessary illustrative examples. We ha
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37

Florentin, Smarandache, Ali Mumtaz, Naz Munazza, and Shabir Muhammad. "Soft Neutrosophic Left Almost Semigroup." May 22, 2014. https://doi.org/10.5281/zenodo.49156.

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 In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LA-semigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutrosophic ideals respectively. We have found some new notions related to the strong or pure part of neutrosophy and we give explaination with necessary illustrative examples. We have also given rigo
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38

Kaviyarasu, M., Mohammed Alqahtani, M. Rajeshwari, and Kholood Alnefai. "Fermatean Neutrosophic Soft Structure and its Ideals in Hyper BCK-Algebras." Contemporary Mathematics, February 27, 2025, 1478–500. https://doi.org/10.37256/cm.6220255814.

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The goal of this paper is to investigate the use of fermatean neutrosophic soft sets (FNSSs) in the context of hyper BCK-algebras. While examining their characteristics and connections, it presents several ideas, including fermatean neutrosophic soft hyper BCK-ideals (FNSH BCK-ideals), fermatean neutrosophic soft weak hyper BCK-ideals (FNSWH BCK-ideals), fermatean neutrosophic softs-weak hyper BCK-ideals (FNSs-WH BCK-ideals), and fermatean neutrosophic soft strong hyper BCK-ideals (FNSSH BCK-ideals). The criteria under which an FNSWH BCK-ideal can be categorized as an FNSs-WH BCK-ideal are als
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39

Siva, Ranjini J., and V. Mahalakshmi. "Neutrosophic Fuzzy Strong Bi-ideals of Near-Subtraction Semigroups." February 11, 2022. https://doi.org/10.5281/zenodo.6041298.

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The theory of Neutrosophy fuzzy set is the extension of the fuzzy set that deals with imprecise and indeterminate data Neutrosophy is a new branch of Philosophy. We already conceptualized the Neutrosophic fuzzy bi-ideals of Near –subtraction Semigroups(NFBI).In this article, We extend our study to strong bi-ideals. We examine some of its fundamentals and algebraic structures. Our aim of this manuscript are given as follows: (i)To explore the new ideas in Neutrosophic fuzzy Near-subtraction semigroups of said bi-ideals and strong bi-ideals. (ii)To examine the some basic properties and fun
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40

Faiz, Muhammad Khan, Khan Madad, and Ihsanullah. "Classification of Ordered Semigroups Through Neutrosophic Generalized bi-ideals with Applications." October 2, 2022. https://doi.org/10.5281/zenodo.7135401.

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An icebreaking theory known as neutrosophic theory opened a new direction for researchers of philosophy, logics, set theory and probability/statistics. Neutrosophy put the point base for a entire household of new mathematical speculations that summarized classical and fuzzy correspondence theories. In this article, we introduced the conception of neutrosophic fuzzy ideal theory of ordered semigroups based on belongs to relation and quasi-coincident with relation. Particularly, neutrosophic fuzzy generalized bi-ideal (resp. bi-ideal) of type (∈, ∈ ∨q) have been developed and detail
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41

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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42

Mumtaz, Ali, Muhammad Shabir, Munazza Naz, and Florentin Smarandache. "Neutrosophic Left Almost Semigroup." Neutrosophic Sets and Systems 3, 2014 (May 4, 2014). https://doi.org/10.5281/zenodo.571537.

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In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties of neutrosophic LA-semigroup in this paper.
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43

Tahan, Madeleine Al, та Bijan Davvaz. "Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra". International Journal of Neutrosophic Science, 2020, 44–53. http://dx.doi.org/10.54216/ijns.030105.

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The connection between neutrosophy and algebra has been of great interest with respect to many researchers. The objective of this paper is to provide a connection between neutrosophic ℵ−structures and subtraction algebras. In this regard, we introduce the concept of neutrosophic ℵ−ideals in subtraction algebra. Moreover, we study its properties and find a necessary and sufficient condition for a neutrosophic ℵ−structure to be a neutrosophic ℵ−ideal.
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44

R, Binu. "Neutrosophic Quotient Algebra." International Journal of Neutrosophic Science, 2019, 83–89. http://dx.doi.org/10.54216/ijns.000204.

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The algebraic properties of neutrosphic ideals over algebra, isomorphism properties of neutrosophic ideal and neutrosophic modules over algebra are discussed in this paper. Some of the charactrisations of Neutrosophic quotient algebra are derived and the role of algebraic structures is studied in the context of neutrosophic set. This paper expands the definition of quotient algebra within the context of neutrosophical set.
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45

Binu, R. "Neutrosophic Quotient Algebra." International Journal of Neutrosophic Science 0 / 2019 (December 1, 2019). https://doi.org/10.5281/zenodo.4018986.

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The algebraic properties of neutrosphic ideals over algebra, isomorphism properties of neutrosophic ideal and neutrosophic modules over algebra are discussed in this paper. Some of the charactrisations of Neutrosophic quotient algebra are derived and the role of algebraic structures is studied in the context of neutrosophic set. This paper expands the definition of quotient algebra within the context of neutrosophical set.
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46

Madeleine, Al Tahan, та Davvaz Bijan. "Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra". 18 серпня 2020. https://doi.org/10.5281/zenodo.3989450.

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The connection between neutrosophy and algebra has been of great interest with respect to many researchers. The objective of this paper is to provide a connection between neutrosophic ℵ−structures and subtraction algebras. In this regard, we introduce the concept of neutrosophic ℵ−ideals in subtraction algebra. Moreover, we study its properties and find a necessary and sufficient condition for a neutrosophic ℵ−structure to be a neutrosophic ℵ−ideal. 
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47

H., Al Akara, Vimala J., and Al-Tahan M. "Some Results on Single Valued Neutrosophic Bi-ideals in Ordered Semigroups." September 7, 2021. https://doi.org/10.5281/zenodo.5486097.

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The importance of the theory of neutrosophy is due to its connections with several fields of sciences, engineering, and technology. So, the aim of this paper is to relate neutrosophy with some algebraic structures mainly the ordered semigroups. In this regard, we define single valued neutrosophic sets in ordered semigroups. More precisely, we study single valued neutrosophic ideals of ordered semigroups and single valued neutrosophic bi-ideals of ordered semigroups.
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48

Rajab, Ali Borzooei, Sabet kish Mahdi, and B. Jun Y. "Neutrosophic LI-ideals in lattice implication algebras." February 5, 2020. https://doi.org/10.5281/zenodo.3640880.

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The notion of neutrosophic set theory is applied to lattice implication algebras, and the concept of neutrosophic LI-ideals and neutrosophic lattice ideals in a lattice implication algebra are introduced. Several properties are investigated. Relationships between a neutrosophic LI-ideal and a neutrosophic lattice ideal are established, and conditions for a neutrosophic lattice ideal to be a neutrosophic LI-ideal are provided. Characterizations of a neutrosophic LI-ideal are discussed. The properties of implication homomorphism of lattice implication algebras related to neutrosophic LI-ideals a
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49

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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50

A., A. Salama, and Smarandache Florentin. "Neutrosophic Ideal Theory Neutrosophic Local Function and Generated Neutrosophic Topology." September 2, 2014. https://doi.org/10.5281/zenodo.30218.

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In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new nutrosophic topology from the original one.
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