Submit Your Paper
  1. Home
  2. Journals
  3. International Journal of Neutrosophic Science

International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)
Submit Your Paper

Journal Menu

Homepage Journal Overview Editorial Board Submitting Articles Indexing & Abstracting

Journal Volumes

International Journal of Neutrosophic Science

Volume 23 , Issue 3 , PP: 18-28, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

New type of Diophantine neutrosophic aggregation operators and its extension

M. Palanikumar 1 * , K. Arulmozhi 2 , K. Sundareswari 3 , Aiyared Iampan 4

  • 1 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India - (palanimaths86@gmail.com)
  • 2 Department of Mathematics, Bharath Institute of Higher Education and Research, Tamil Nadu, Chennai-600073, India - (arulmozhiems@gmail.com)
  • 3 Department of Mathematics, Al-Ameen Engineering College, Erode. - (k.sundareswari@gmail.com)
  • 4 Fuzzy Algebras and Decision-Making Problems Research Unit, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand. - (aiyared.ia@up.ac.th)

    • Doi: https://doi.org/10.54216/IJNS.230302

    Received: July 28, 2023 Revised: September 18, 2023 Accepted: January 15, 2024
    Abstract

    We introduce the concept of new type of Diophantine neutrosophic set. A Diophatine neutrosophic set is the new type of a neutrosophic set and Diophatine fuzzy set (DioFS). We discuss Diophantine neutrosophic weighted averaging (DioNWA), Diophantine neutrosophic weighted geometric (DioNWG), generalized Diophantine neutrosophic weighted averaging(GDioNWA), generalized Diophantine neutrosophic weighted geometric (GDioNWG). In this article, we define the Euclidean distance (ED), Hamming distance (HD) and operator laws. By analyzing new type of Diophantine neutrosophic set through algebraic operations, we discuss its properties.

    Keywords :

    DioNWA , DioNWG , GDioNWA , GDioNWG.

    References

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

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

    [3] R. R. Yager, Pythagorean membership grades in multi criteria decision-making, IEEE Trans. Fuzzy Systems, 22, (2014), 958-965.

    [4] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani and T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, Journal of Intelligent and Fuzzy Systems, 36, (2019), 2829-284.

    [5] B.C. Cuong and V. Kreinovich, Picture fuzzy sets a new concept for computational intelligence problems, in Proceedings of 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, (2013), 1-6.

    [6] P. Liu, G. Shahzadi, M. Akram, Specific types of picture fuzzy Yager aggregation operators for decisionmaking, International Journal of Computational Intelligence Systems, 13(1), (2020), 1072-1091.

    [7] W.F. Liu, J. Chang, X. He, Generalized Pythagorean fuzzy aggregation operators and applications in decision making, Control Decis. 31, (2016), 2280-2286.

    [8] X. Peng, and Y. Yang, Fundamental properties of interval valued Pythagorean fuzzy aggregation operators,International Journal of Intelligent Systems, (2015), 1-44.

    [9] K.G. Fatmaa, K. Cengiza, Spherical fuzzy sets and spherical fuzzy TOPSIS method, Journal of Intelligent and Fuzzy Systems, 36(1), (2019), 337-352.

    [10] X. D. Peng and J. Dai, Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function, Neural Computing and Applications, 29(10), (2018), 939-954.

    [11] X. Lhang and L. Xu, Extension of TOPSIS to multiple criteria decision-making with Diophantine Pythagorean fuzzy sets, International Journal of Intelligent Systems, 29, (2014), 1061-1078.

    [12] C. L. Hwang, K. Yoon, Multiple attributes decision-making methods and applications, Springer, Berlin Heidelberg, 1981.

    [13] M. Riaz and M. R. Hashmi, Linear Diophantine fuzzy set and its applications towards multi-attribute decision making problems, Journal of Intelligent and Fuzzy Systems, 37(4), (2019), 5417-5439.

    [14] M Palanikumar, K Arulmozhi, A Iampan, Multi criteria group decision making based on VIKOR and TOPSIS methods for Fermatean fuzzy soft with aggregation operators, ICIC Express Letters 16 (10), 2022, 1129–1138.

    [15] M Palanikumar, K Arulmozhi, MCGDM based on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators, Neutrosophic Sets and Systems, 2022, 538-555.

    [16] A. Al Quran, A. G. Ahmad, F. Al Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, International Journal of Neutrosophic Science, 20(2), 2023, 08-19.

    [17] F. Al Sharqi, M. U. Romdhini, A. Al-Quran, Group decision making based on aggregation operator and score function of Q-neutrosophic soft matrix, Journal of Intelligent and Fuzzy Systems, 45, 2023, 305–321.

    [18] Broumi, S., Sundareswaran, R., Shanmugapriya, M., Bakali, A., Talea, M. Theory and Applications of Fermatean Neutrosophic Graphs. Neutrosophic Sets and Systems, 50, (2022), 248-286.

    [19] Broumi, S., Mohanaselvi, S., Witczak, T., Talea, M., Bakali, A., Smarandache, F. Complex fermatean neutrosophic graph and application to decision making. Decision Making: Applications in Management and Engineering, 6(1), (2023), 474-501.

    Cite This Article As :
    Palanikumar, M.. , Arulmozhi, K.. , Sundareswari, K.. , Iampan, Aiyared. New type of Diophantine neutrosophic aggregation operators and its extension. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 18-28. DOI: https://doi.org/10.54216/IJNS.230302
    Palanikumar, M. Arulmozhi, K. Sundareswari, K. Iampan, A. (2024). New type of Diophantine neutrosophic aggregation operators and its extension. International Journal of Neutrosophic Science, (), 18-28. DOI: https://doi.org/10.54216/IJNS.230302
    Palanikumar, M.. Arulmozhi, K.. Sundareswari, K.. Iampan, Aiyared. New type of Diophantine neutrosophic aggregation operators and its extension. International Journal of Neutrosophic Science , no. (2024): 18-28. DOI: https://doi.org/10.54216/IJNS.230302
    Palanikumar, M. , Arulmozhi, K. , Sundareswari, K. , Iampan, A. (2024) . New type of Diophantine neutrosophic aggregation operators and its extension. International Journal of Neutrosophic Science , () , 18-28 . DOI: https://doi.org/10.54216/IJNS.230302
    Palanikumar M. , Arulmozhi K. , Sundareswari K. , Iampan A. [2024]. New type of Diophantine neutrosophic aggregation operators and its extension. International Journal of Neutrosophic Science. (): 18-28. DOI: https://doi.org/10.54216/IJNS.230302
    Palanikumar, M. Arulmozhi, K. Sundareswari, K. Iampan, A. "New type of Diophantine neutrosophic aggregation operators and its extension," International Journal of Neutrosophic Science, vol. , no. , pp. 18-28, 2024. DOI: https://doi.org/10.54216/IJNS.230302

    Article Statistics

    View
    55432
    Download
    601

    Download