ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 25Issue 3PP: 144-154 • 2025

Several arithmetic operations on neutrosophics type-2 fuzzy sets

Brahim Ziane 1* ,
Soheyb Milles 2
1Laboratoire de Math´ematiques et Physique Appliqu´ees, ´E cole Normale Sup´erieure de Bousaada 28001, Algeria
2Department of Mathematics, Institute of Science, University Center of Barika, Algeria
* Corresponding Author.
Received: February 24, 2024 Revised: May 26, 2024 Accepted: September 27, 2024

Abstract

In this paper, we explore the theoretical foundations of neutrosophics type-2 fuzzy sets by investigating its algebraic properties, demonstrating how neutrosophics type-2 fuzzy sets can generalize and extend existing operations in Type-1 and traditional Type-2 fuzzy sets. We also provide illustrative examples to clarify the practical applications of these operations, showcasing the potential of neutrosophics type-2 fuzzy sets in areas requiring sophisticated decision-making tools and uncertainty management.

Keywords

Type-2 fuzzy set Intuitionistic type-2 fuzzy set Neutrosophics type-2 fuzzy set

References

[1] Ravi P Agarwal, Soheyb Milles, Brahim Ziane, Abdelaziz Mennouni, and Lemnaouar Zedam. Ideals and filters on neutrosophic topologies generated by neutrosophic relations. Axioms, 13(5):292, 2024.

[2] Janet Aisbett, John T Rickard, and David G Morgenthaler. Type-2 fuzzy sets as functions on spaces. IEEE Transactions on Fuzzy Systems, 18(4):841–844, 2010.

[3] Abdelaziz Amroune and Brahim Ziane. More on intuitionistic fuzzy sublattices and their ideals. 2019.

[4] Bui Cong Cuong, Vladik Kreinovitch, and Roan Thi Ngan. A classification of representable t-norm operators for picture fuzzy sets. In 2016 eighth international conference on knowledge and systems engineering (KSE), pages 19–24. IEEE, 2016.

[5] Glad Deschrijver, Chris Cornelis, and Etienne E Kerre. On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE transactions on fuzzy systems, 12(1):45–61, 2004.

[6] Joseph A Goguen. L-fuzzy sets. Journal of mathematical analysis and applications, 18(1):145–174, 1967.

[7] A UNIFYING FIELD IN LOGICS and NEUTROSOPHIC LOGIC. Florentin smarandache. 2007.

[8] JerryMMendel. Advances in type-2 fuzzy sets and systems. Information sciences, 177(1):84–110, 2007.

[9] Jerry M. Mendel. Type-2 fuzzy sets and systems: a retrospective. Informatik-Spektrum, 38(6), 2015.

[10] F Neutrosophy Smarandache. Neutrisophic property, sets, and logic, 1998.

[11] Florentin Smarandache. n-valued refined neutrosophic logic and its applications to physics. Infinite Study, 4:143–146, 2013.

[12] Zdenko Tak´aˇc. Aggregation of fuzzy truth values. Information Sciences, 271:1–13, 2014.

[13] Haibin Wang, Florentin Smarandache, Yanqing Zhang, and Rajshekhar Sunderraman. Single valued neutrosophic sets. Infinite study, 12, 2010.

[14] Hai-Long Yang, Zhi-Lian Guo, Yanhong She, and Xiuwu Liao. On single valued neutrosophic relations. Journal of Intelligent & Fuzzy Systems, 30(2):1045–1056, 2016.

[15] Lotfi A Zadeh. Fuzzy sets. Information and control, 8(3):338–353, 1965.

[16] Lotfi A Zadeh. The concept of a linguistic variable and its application to approximate reasoning—i. Information sciences, 8(3):199–249, 1975.

[17] Lotfi A Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 100:9–34, 1999.

[18] Brahim Ziane and Abdelaziz Amroune. Representation and construction of intuitionistic fuzzy tpreorders and fuzzy weak t-orders. Discussiones Mathematicae: General Algebra & Applications, 41(1), 2021.

 

Cite This Article

Choose your preferred format

format_quote
Ziane, Brahim, Milles, Soheyb. "Several arithmetic operations on neutrosophics type-2 fuzzy sets." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 3, 2025, pp. 144-154. DOI: https://doi.org/10.54216/IJNS.250314
Ziane, B., Milles, S. (2025). Several arithmetic operations on neutrosophics type-2 fuzzy sets. International Journal of Neutrosophic Science, Volume 25(Issue 3), 144-154. DOI: https://doi.org/10.54216/IJNS.250314
Ziane, Brahim, Milles, Soheyb. "Several arithmetic operations on neutrosophics type-2 fuzzy sets." International Journal of Neutrosophic Science Volume 25, no. Issue 3 (2025): 144-154. DOI: https://doi.org/10.54216/IJNS.250314
Ziane, B., Milles, S. (2025) 'Several arithmetic operations on neutrosophics type-2 fuzzy sets', International Journal of Neutrosophic Science, Volume 25(Issue 3), pp. 144-154. DOI: https://doi.org/10.54216/IJNS.250314
Ziane B, Milles S. Several arithmetic operations on neutrosophics type-2 fuzzy sets. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 3):144-154. DOI: https://doi.org/10.54216/IJNS.250314
B. Ziane, S. Milles, "Several arithmetic operations on neutrosophics type-2 fuzzy sets," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 3, pp. 144-154, 2025. DOI: https://doi.org/10.54216/IJNS.250314
Digital Archive Ready