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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 24 , Issue 4 , PP: 293-314, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Product of rings based on neutrosophic sets

Aiyared Iampan 1 * , S. R. Vidhya 2 , N. Rajesh 3 , B. Brundha 4

  • 1 Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand - (aiyared.ia@up.ac.th)
  • 2 Department of Mathematics, Bon Secours College for Women (affiliated to Bharathidasan University), Thanjavur-613006, Tamilnadu, India - (svsubi16@gmail.com)
  • 3 Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamilnadu, India - (nrajesh topology@yahoo.co.in)
  • 4 Department of Mathematics, Government Arts College for Women, Orathanadu-614625, Tamilnadu, India - (brindamithunraj@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.240421

    Received: September 08, 2023 Revised: February 19, 2024 Accepted: June 02, 2024
    Abstract

    In this paper, we introduce the notion of the intrinsic product of neutrosophic sets, and some related properties are investigated. Characterizations of neutrosophic subrings, neutrosophic ideals, neutrosophic quasi-ideals, and neutrosophic bi-ideals are given.

    Keywords :

    ring , neutrosophic subring , neutrosophic ideal , neutrosophic quasi-ideal , neutrosophic bi-ideal.

    References

    [1] B. Ahmad and A. Kharal, On fuzzy soft sets, Advances in Fuzzy Systems, 2009, (2009), Article ID 586507, 6 pages.

    [2] K. T. Atanassov, Intuitionistic sets, Fuzzy Sets and Systems, 20(1), (1986), 87-96.

    [3] M. Atef, M. I. Ali, and T. M. Al-Shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their applications, Computational and Applied Mathematics, 40(4), (2021), 115.

    [4] N. Caˇgman, S. Enginoˇglu, and F. Citak, Fuzzy soft set theory and its application, Iranian Journal of Fuzzy Systems, 8(3), (2011), 137-147.

    [5] V. Cetkin and H. Aygun, An approach to neutrosophic ideals, Universal Journal of Mathematics and Applications, 1(2), (2018), 132-136.

    [6] V. Cetkin and H. Aygun, An approach to neutrosophic subrings, Sakarya University Journal of Science, 23(3), (2019), 472-477.

    [7] H. Garg and K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Computing, 22(15), (2018), 4959-4970.

    [8] H. Garg and K. Kumar, Distance measures for connection number sets based on set pair analysis and its applications to decision-making process, Applied Intelligence, 48(10), (2018), 3346-3359.

    [9] H. Garg and S. Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators, Iranian Journal of Fuzzy Systems, 15, (2018), 69-93.

    [10] F. Smarandache, A unifying field in logics, neutrosophy neutrosophic probability, set and logic, American Research Press, Rehoboth, 1999.

    [11] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965), 338-353.

    Cite This Article As :
    Iampan, Aiyared. , R., S.. , Rajesh, N.. , Brundha, B.. Product of rings based on neutrosophic sets. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 293-314. DOI: https://doi.org/10.54216/IJNS.240421
    Iampan, A. R., S. Rajesh, N. Brundha, B. (2024). Product of rings based on neutrosophic sets. International Journal of Neutrosophic Science, (), 293-314. DOI: https://doi.org/10.54216/IJNS.240421
    Iampan, Aiyared. R., S.. Rajesh, N.. Brundha, B.. Product of rings based on neutrosophic sets. International Journal of Neutrosophic Science , no. (2024): 293-314. DOI: https://doi.org/10.54216/IJNS.240421
    Iampan, A. , R., S. , Rajesh, N. , Brundha, B. (2024) . Product of rings based on neutrosophic sets. International Journal of Neutrosophic Science , () , 293-314 . DOI: https://doi.org/10.54216/IJNS.240421
    Iampan A. , R. S. , Rajesh N. , Brundha B. [2024]. Product of rings based on neutrosophic sets. International Journal of Neutrosophic Science. (): 293-314. DOI: https://doi.org/10.54216/IJNS.240421
    Iampan, A. R., S. Rajesh, N. Brundha, B. "Product of rings based on neutrosophic sets," International Journal of Neutrosophic Science, vol. , no. , pp. 293-314, 2024. DOI: https://doi.org/10.54216/IJNS.240421

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