International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 24 , Issue 3 , PP: 220-232, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.

M. Palanikumar 1 , T. T. Raman 2 , A. Swaminathan 3 , Aiyared Iampan 4

  • 1 Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 602105, India - (palanimaths86@gmail.com)
  • 2 Department of Mathematics, St. Joseph’s Institute of Technology, OMR, Chennai-600119, India - (ramanstat@gmail.com)
  • 3 Department of Mathematics, Agni College of Technology, Thalambur, Chennai-600130, India. - (nathanswamin@gmail.com)
  • 4 Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. - (aiyared.ia@up.ac.th)
  • Doi: https://doi.org/10.54216/IJNS.240319

    Received: september 08, 2023 Revised: February 05, 2024 Accepted: March 01, 2024
    Abstract

    The purpose of this article is to present a novel approach to the (δ,ε)  interval-valued neutrosophic set (IVNS). This is an extension of the IVNS. As a result of this article, we will discuss the concept of (δ,ε)   interval valued neutrosophic weighted averaging (IVNWA), (δ,ε)  interval-valued neutrosophic weighted geometric (IVNWG), (δ,ε)  generalized interval-valued neutrosophic weighted averaging (GIVNWA) and (δ,ε)  generalized interval-valued neutrosophic weighted geometric (GIVNWG). Additionally, the (δ,ε) IVNS approach is characterized by idempotency, boundedness, commutativity and monotonicity.

    Keywords :

    (&delta , ,&epsilon , ) IVNWA, (&delta , ,&epsilon , ) IVNWG, G (&delta , ,&epsilon , ) IVNWA, G (&delta , ,&epsilon , ) IVNWAG.

    References

    [1] L. A. Ladeh, 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 decision-making, 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] SG Quek, H Garg, G Selvachandran, M Palanikumar, K Arulmozhi,VIKOR and TOPSIS framework with a truthfuldistance measure for the (t, s)-regulated interval-valued neutrosophic soft set, Soft Computing, 1-27, 2023.

    [11] 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), 1129–1138, 2022.

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

    [13] M Palanikumar, S Broumi, Square root (δ, ε)phantine neutrosophic normal interval-valued sets and their aggregated operators in application to multiple attribute decision making, International Journal of Neutrosophic Science, 4, 2022.

    [14] D.F. Li, Multi-attribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets, Expert Syst. Appl. 37, (2010), 8673-8678.

    [15] X. Peng, H. Yuan, Fundamental properties of Pythagorean fuzzy aggregation operators, Fundam. Inform. 147, (2016), 415-446.

    [16] Tansu Temel, Salih Berkan Aydemir,Yasar Hoscan, Power Muirhead mean in spherical normal fuzzy environment and its applications to multi-attribute decision-making, Complex and Intelligent Systems, (2022), 1-19.

    [17] K. Ullah, H. Garg, T. Mahmood, N. Jan, Z. Ali, Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making, Soft Comput. 24, (2020), 1647-1659.

    [18] K. Ullah, T. Mahmood, H. Garg, Evaluation of the performance of search and rescue robots using T-spherical fuzzy hamacher aggregation operators, Int. J. Fuzzy Syst. 22, (2020), 570-582.

    [19] R.N. Xu and C.L. Li, Regression prediction for fuzzy time series, Appl. Math. J. Chinese Univ., 16, (2001), 451-461.

    [20] Z. Xu, R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst. 35, (2006), 417-433.

    [21] S. Zeng, W. Sua, Intuitionistic fuzzy ordered weighted distance operator, Knowl. Based Syst. 24, (2011), 1224-1232.

    [22] M Palanikumar, K Arulmozhi, Novel possibility Pythagorean interval valued fuzzy soft set method for a decision making, TWMS J. App. and Eng. Math. V.13, N.1, 2023, pp. 327-340.

    [23] M Palanikumar, N Kausar, H Garg, A Iampan, S Kadry, M Sharaf, Medical robotic engineering selection based on square root neutrosophic normal interval-valued sets and their aggregated operators, AIMS Mathematics, 8(8), 2023, 17402-17432.

    [24] M. Palanikumar, K. Arulmozhi, and C. Jana, Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued aggregation operators, Comp. Appl. Math. 41(90), (2022), 1-27.

    Cite This Article As :
    Palanikumar, M.. , T., T.. , Swaminathan, A.. , Iampan, Aiyared. Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 220-232. DOI: https://doi.org/10.54216/IJNS.240319
    Palanikumar, M. T., T. Swaminathan, A. Iampan, A. (2024). Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.. International Journal of Neutrosophic Science, (), 220-232. DOI: https://doi.org/10.54216/IJNS.240319
    Palanikumar, M.. T., T.. Swaminathan, A.. Iampan, Aiyared. Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.. International Journal of Neutrosophic Science , no. (2024): 220-232. DOI: https://doi.org/10.54216/IJNS.240319
    Palanikumar, M. , T., T. , Swaminathan, A. , Iampan, A. (2024) . Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.. International Journal of Neutrosophic Science , () , 220-232 . DOI: https://doi.org/10.54216/IJNS.240319
    Palanikumar M. , T. T. , Swaminathan A. , Iampan A. [2024]. Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.. International Journal of Neutrosophic Science. (): 220-232. DOI: https://doi.org/10.54216/IJNS.240319
    Palanikumar, M. T., T. Swaminathan, A. Iampan, A. "Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.," International Journal of Neutrosophic Science, vol. , no. , pp. 220-232, 2024. DOI: https://doi.org/10.54216/IJNS.240319