On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras

Bavanari Satyanarayana; Kamidi Madhavi; Shake Baji; Dasari Ramesh

doi:doi:10.11648/j.ajam.20261405.13

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On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras

Bavanari Satyanarayana

, Kamidi Madhavi

, Shake Baji

, Dasari Ramesh

Published in American Journal of Applied Mathematics (Volume 14, Issue 5)

Received: 18 July 2026 Accepted: 30 July 2026 Published: 20 September 2026

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Abstract

In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characterize neutrosophic fuzzy ideals through their level sets and show that a neutrosophic fuzzy set is a neutrosophic fuzzy ideal if and only if its corresponding level sets are also ideals. We also provide sufficient conditions under which the neutrosophic translation of a neutrosophic fuzzy ideal forms a neutrosophic fuzzy subalgebra. In addition, we introduce the concept of an extension of a neutrosophic fuzzy ideal and prove that the neutrosophic translation of a neutrosophic fuzzy ideal is a neutrosophic fuzzy ideal extension. An illustrative example is presented to demonstrate that not every neutrosophic fuzzy ideal extension is obtained as a translation of a neutrosophic fuzzy ideal. Moreover, we define the multiplication of neutrosophic fuzzy ideals and investigate its properties in B-algebras. We prove that the multiplication of neutrosophic fuzzy ideals is also a neutrosophic fuzzy ideal under appropriate conditions. The results establish meaningful relationships among neutrosophic fuzzy ideals, translations, level sets, extensions, and multiplication in B-algebras. These findings contribute to the development of neutrosophic fuzzy algebraic structures and provide a systematic framework for further investigations of ideals and their associated operations in B-algebras. The proposed characterizations also clarify structural behavior and broaden the existing theoretical framework for neutrosophic fuzzy algebraic systems.

Published in	American Journal of Applied Mathematics (Volume 14, Issue 5)
DOI	10.11648/j.ajam.20261405.13
Page(s)	295-302
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

B-algebra, Translations, Multiplications, Neutrosophic Fuzzy Ideal, Neutrosophic Fuzzy Ideal Extension

References

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[4]	T. Senapati, C.S. Kim, M. Bhowmik, and M. Pal, Cubic subalgebras and cubic closed ideals of B-algebras, Fuzzy Inf. Eng., 7 (2015), pp. 129-149. https://.org/10.1016/j.fiae.2015.05.001
[5]	T. Senapati, M. Bhowmik, M. Pal, and B. Davvaz, Fuzzy translations of fuzzy H-ideals in BCK/BCI-algebras, J. Indones. Math. Soc., 21 (2015), pp. 45-58. https://doi.org/ 10.22342/jims.21.1.200.45-58
[6]	T. Senapati, Translations of intuitionistic fuzzy B-algebras, Fuzzy Inf. Eng., 7 (2015), pp. 389-404. https://doi.org/10.1016/j.fiae.2015.11.001
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[9]	Bavanari Satyanarayana, Kamidi Madhavi, S. Baji, and Dasari Ramesh, Translations of neutrosophic fuzzy subalgebras of B-algebras, (In press).
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[16]	A.B. Saeid, Fuzzy topological B-algebras, Int. J. Fuzzy Syst., 8 (2006), pp. 160-164. https://api.semanticscholar.org/CorpusID:6153837
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APA Style

Satyanarayana, B., Madhavi, K., Baji, S., Ramesh, D. (2026). On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras. American Journal of Applied Mathematics, 14(5), 295-302. https://doi.org/10.11648/j.ajam.20261405.13

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ACS Style

Satyanarayana, B.; Madhavi, K.; Baji, S.; Ramesh, D. On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras. Am. J. Appl. Math. 2026, 14(5), 295-302. doi: 10.11648/j.ajam.20261405.13

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AMA Style

Satyanarayana B, Madhavi K, Baji S, Ramesh D. On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras. Am J Appl Math. 2026;14(5):295-302. doi: 10.11648/j.ajam.20261405.13

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@article{10.11648/j.ajam.20261405.13,
  author = {Bavanari Satyanarayana and Kamidi Madhavi and Shake Baji and Dasari Ramesh},
  title = {On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras},
  journal = {American Journal of Applied Mathematics},
  volume = {14},
  number = {5},
  pages = {295-302},
  doi = {10.11648/j.ajam.20261405.13},
  url = {https://doi.org/10.11648/j.ajam.20261405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261405.13},
  abstract = {In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characterize neutrosophic fuzzy ideals through their level sets and show that a neutrosophic fuzzy set is a neutrosophic fuzzy ideal if and only if its corresponding level sets are also ideals. We also provide sufficient conditions under which the neutrosophic translation of a neutrosophic fuzzy ideal forms a neutrosophic fuzzy subalgebra. In addition, we introduce the concept of an extension of a neutrosophic fuzzy ideal and prove that the neutrosophic translation of a neutrosophic fuzzy ideal is a neutrosophic fuzzy ideal extension. An illustrative example is presented to demonstrate that not every neutrosophic fuzzy ideal extension is obtained as a translation of a neutrosophic fuzzy ideal. Moreover, we define the multiplication of neutrosophic fuzzy ideals and investigate its properties in B-algebras. We prove that the multiplication of neutrosophic fuzzy ideals is also a neutrosophic fuzzy ideal under appropriate conditions. The results establish meaningful relationships among neutrosophic fuzzy ideals, translations, level sets, extensions, and multiplication in B-algebras. These findings contribute to the development of neutrosophic fuzzy algebraic structures and provide a systematic framework for further investigations of ideals and their associated operations in B-algebras. The proposed characterizations also clarify structural behavior and broaden the existing theoretical framework for neutrosophic fuzzy algebraic systems.},
 year = {2026}
}

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TY  - JOUR
T1  - On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras
AU  - Bavanari Satyanarayana
AU  - Kamidi Madhavi
AU  - Shake Baji
AU  - Dasari Ramesh
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.ajam.20261405.13
DO  - 10.11648/j.ajam.20261405.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 295
EP  - 302
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20261405.13
AB  - In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characterize neutrosophic fuzzy ideals through their level sets and show that a neutrosophic fuzzy set is a neutrosophic fuzzy ideal if and only if its corresponding level sets are also ideals. We also provide sufficient conditions under which the neutrosophic translation of a neutrosophic fuzzy ideal forms a neutrosophic fuzzy subalgebra. In addition, we introduce the concept of an extension of a neutrosophic fuzzy ideal and prove that the neutrosophic translation of a neutrosophic fuzzy ideal is a neutrosophic fuzzy ideal extension. An illustrative example is presented to demonstrate that not every neutrosophic fuzzy ideal extension is obtained as a translation of a neutrosophic fuzzy ideal. Moreover, we define the multiplication of neutrosophic fuzzy ideals and investigate its properties in B-algebras. We prove that the multiplication of neutrosophic fuzzy ideals is also a neutrosophic fuzzy ideal under appropriate conditions. The results establish meaningful relationships among neutrosophic fuzzy ideals, translations, level sets, extensions, and multiplication in B-algebras. These findings contribute to the development of neutrosophic fuzzy algebraic structures and provide a systematic framework for further investigations of ideals and their associated operations in B-algebras. The proposed characterizations also clarify structural behavior and broaden the existing theoretical framework for neutrosophic fuzzy algebraic systems.
VL  - 14
IS  - 5
ER  -

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Author Information

Bavanari Satyanarayana

Department of Mathematics, Acharya Nagarjuna University, Guntur, India

Contact Email

http://orcid.org/0000-0002-1265-4189
Kamidi Madhavi

Department of Mathematics, S.W.R Government Degree college for Girls, Kalikiri, India

Contact Email

http://orcid.org/0009-0003-0468-2766
Shake Baji

Department of Mathematics, Vasireddy Venkatadri International Technological University, Nambur, India

Contact Email

http://orcid.org/0000-0002-6090-8083
Dasari Ramesh

Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaih Educational Fondation, Vaddeswaram, India

Contact Email

http://orcid.org/0000-0003-1473-6804

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Plain Text BibTeX RIS

APA Style

Satyanarayana, B., Madhavi, K., Baji, S., Ramesh, D. (2026). On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras. American Journal of Applied Mathematics, 14(5), 295-302. https://doi.org/10.11648/j.ajam.20261405.13

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ACS Style

Satyanarayana, B.; Madhavi, K.; Baji, S.; Ramesh, D. On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras. Am. J. Appl. Math. 2026, 14(5), 295-302. doi: 10.11648/j.ajam.20261405.13

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AMA Style

Satyanarayana B, Madhavi K, Baji S, Ramesh D. On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras. Am J Appl Math. 2026;14(5):295-302. doi: 10.11648/j.ajam.20261405.13

Copy | Download

@article{10.11648/j.ajam.20261405.13,
  author = {Bavanari Satyanarayana and Kamidi Madhavi and Shake Baji and Dasari Ramesh},
  title = {On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras},
  journal = {American Journal of Applied Mathematics},
  volume = {14},
  number = {5},
  pages = {295-302},
  doi = {10.11648/j.ajam.20261405.13},
  url = {https://doi.org/10.11648/j.ajam.20261405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261405.13},
  abstract = {In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characterize neutrosophic fuzzy ideals through their level sets and show that a neutrosophic fuzzy set is a neutrosophic fuzzy ideal if and only if its corresponding level sets are also ideals. We also provide sufficient conditions under which the neutrosophic translation of a neutrosophic fuzzy ideal forms a neutrosophic fuzzy subalgebra. In addition, we introduce the concept of an extension of a neutrosophic fuzzy ideal and prove that the neutrosophic translation of a neutrosophic fuzzy ideal is a neutrosophic fuzzy ideal extension. An illustrative example is presented to demonstrate that not every neutrosophic fuzzy ideal extension is obtained as a translation of a neutrosophic fuzzy ideal. Moreover, we define the multiplication of neutrosophic fuzzy ideals and investigate its properties in B-algebras. We prove that the multiplication of neutrosophic fuzzy ideals is also a neutrosophic fuzzy ideal under appropriate conditions. The results establish meaningful relationships among neutrosophic fuzzy ideals, translations, level sets, extensions, and multiplication in B-algebras. These findings contribute to the development of neutrosophic fuzzy algebraic structures and provide a systematic framework for further investigations of ideals and their associated operations in B-algebras. The proposed characterizations also clarify structural behavior and broaden the existing theoretical framework for neutrosophic fuzzy algebraic systems.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras
AU  - Bavanari Satyanarayana
AU  - Kamidi Madhavi
AU  - Shake Baji
AU  - Dasari Ramesh
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.ajam.20261405.13
DO  - 10.11648/j.ajam.20261405.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 295
EP  - 302
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20261405.13
AB  - In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characterize neutrosophic fuzzy ideals through their level sets and show that a neutrosophic fuzzy set is a neutrosophic fuzzy ideal if and only if its corresponding level sets are also ideals. We also provide sufficient conditions under which the neutrosophic translation of a neutrosophic fuzzy ideal forms a neutrosophic fuzzy subalgebra. In addition, we introduce the concept of an extension of a neutrosophic fuzzy ideal and prove that the neutrosophic translation of a neutrosophic fuzzy ideal is a neutrosophic fuzzy ideal extension. An illustrative example is presented to demonstrate that not every neutrosophic fuzzy ideal extension is obtained as a translation of a neutrosophic fuzzy ideal. Moreover, we define the multiplication of neutrosophic fuzzy ideals and investigate its properties in B-algebras. We prove that the multiplication of neutrosophic fuzzy ideals is also a neutrosophic fuzzy ideal under appropriate conditions. The results establish meaningful relationships among neutrosophic fuzzy ideals, translations, level sets, extensions, and multiplication in B-algebras. These findings contribute to the development of neutrosophic fuzzy algebraic structures and provide a systematic framework for further investigations of ideals and their associated operations in B-algebras. The proposed characterizations also clarify structural behavior and broaden the existing theoretical framework for neutrosophic fuzzy algebraic systems.
VL  - 14
IS  - 5
ER  -

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