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 25 , Issue 3 , PP: 92-105, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set

Aiyared Iampan 1 * , M. Palanikumar 2 , M. S. Malchijah Raj 3

  • 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, SRM Valliammai Engineering College, Kattankulathur 603203, Tamilnadu, India - (palanimaths86@gmail.com)
  • 3 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India - (malchijahraj@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.250309

    Received: February 14, 2024 Revised: May 16, 2024 Accepted: September 20, 2024
    Abstract

    We present the neutrosophic interval-valued set applied to the q-rung logarithmic operator (q-RLOANIVS). One might develop a q-rung neutrosophic interval-valued set by extending the Pythagorean interval-valued fuzzy set (PIVFS) and neutrosophic set (NS). We discuss the q-Rlogarithimic operator applied neutrosophic interval-valued weighted averaging (q-RLOANIVWA), q-Rlogarithimic operator applied neutrosophic intervalvalued weighted geometric (q-RLOANIVWG), extended q-Rlogarithimic operator applied neutrosophic intervalvalued weighted averaging (q-RELOANIVWA) and extended q-Rlogarithimic operator applied neutrosophic interval-valued weighted geometric (q-RELOANIVWG). Several algebraic attributes have been established, including distributivity, idempotency, and associativity of q-RLOANIVSs.

    Keywords :

    q-RLOANIVWA , q-RLOANIVWG , q-RELOANIVWA , q-RELOANIVWG

    References

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

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

    [3] Gorzalczany, M., A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21, 1-17, 1987.

    [4] Biswas, R., Vague groups. International Journal of Computational Cognition, 4(2), 20-23, 2006.

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

    [6] Peng, X., Yang, Y., Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. International Journal of Intelligent Systems, 31(5), 444-487, 2016.

    [7] Ashraf, S., Abdullah, S., Mahmood, T., Ghani, F., Mahmood, T., Spherical fuzzy sets and their applications in multi-attribute decision-making problems. J. Intell. Fuzzy Syst., 36, 2829-284, 2019.

    [8] Smarandache, F., Unifying, A., Field in logics neutrosophic logic, multiple valued logic. An International Journal, 8(3), 385-438, 2002.

    [9] Cuong, B.C., Kreinovich, V., 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, 1-6, 2013.

    [10] Palanikumar, M., Arulmozhi, K., Jana, C., Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators. Computational and Applied Mathematics, 41(3), 90, 2022.

    [11] Palanikumar, M., Arulmozhi, K., Jana, C, Pal, M., Multiple attribute decision making spherical vague normal operators and their applications for the selection of farmers. Expert Systems, 40(3), e13188, 2022.

    [12] Palanikumar, M., Arulmozhi, K., MCGDM based on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators. Neutrosophic Sets and Systems, 51, 538-555, 2022.

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

    [14] Palanikumar, M., Iampan, A., Spherical Fermatean interval-valued fuzzy soft set based on multi criteria group decision making. International Journal of Innovative Computing, Information and Control, 18(2), 607-619, 2022.

    [15] Palanikumar, M., Iampan, A., Novel approach to decision making based on type-II extended Fermatean bipolar fuzzy soft sets. International Journal of Innovative Computing, Information and Control, 18(3), 769-781, 2022.

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

    [17] Palanikumar, M., Arulmozhi, K., Iampan, A., 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.

    [18] Quek, S.G., Garg, H., Selvachandran, G., Palanikumar, M., Arulmozhi, K., VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set. Soft Computing, 1-27, 2023.

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

    [20] Ye, J., Similarity measures between interval neutrosophic sets and their applications in Multi-criteria decision-making. Journal of Intelligent and Fuzzy Systems, 26, 165-172, 2014.

    [21] Palanikumar, M., Arulmozhi, K., On intuitionistic fuzzy normal subbisemiring of bisemiring. Nonlinear Studies, 28(3), 717-721, 2021.

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

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

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

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

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

    [27] Ashraf, S., Abdullah, S., Mahmood, T., Spherical fuzzy Dombi aggregation operators and their application in group decision-making problems. J. Amb. Intell. Hum. Comput., 11, 2731-2749, 2020.

    [28] Temel, T., Aydemir, S.B., Hoscan, Y., Power Muirhead mean in spherical normal fuzzy environment and its applications to multi-attribute decision-making. Complex and Intelligent Systems, 1-19, 2022.

    [29] Qiu, Y., Bouraima, M.B., Kiptum, C.K., Ayyildiz, E., Stevic, Z, Badi, I., Ndiema, K.M., Strategies for Enhancing Industry 4.0 Adoption in East Africa: An Integrated Spherical Fuzzy SWARA-WASPAS Approach. J. Ind. Intell., 1(2), 87-100, 2023.

    [30] Choudhary, R., Ashraf, S., Anafi, J., Enhanced industrial control system of decision-making using spherical hesitant fuzzy soft yager aggregation information. Acadlore Trans. Appl. Math. Stat., 1(3), 161-180, 2023.

    [31] Khan, A.A., Mashat, D.S., Dong, K., Evaluating Sustainable Urban Development Strategies through Spherical CRITIC-WASPAS. Analysis. J. Urban Dev. Manag., 3(1), 1-17, 2024.

    Cite This Article As :
    Iampan, Aiyared. , Palanikumar, M.. , S., M.. Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 92-105. DOI: https://doi.org/10.54216/IJNS.250309
    Iampan, A. Palanikumar, M. S., M. (2025). Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set. International Journal of Neutrosophic Science, (), 92-105. DOI: https://doi.org/10.54216/IJNS.250309
    Iampan, Aiyared. Palanikumar, M.. S., M.. Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set. International Journal of Neutrosophic Science , no. (2025): 92-105. DOI: https://doi.org/10.54216/IJNS.250309
    Iampan, A. , Palanikumar, M. , S., M. (2025) . Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set. International Journal of Neutrosophic Science , () , 92-105 . DOI: https://doi.org/10.54216/IJNS.250309
    Iampan A. , Palanikumar M. , S. M. [2025]. Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set. International Journal of Neutrosophic Science. (): 92-105. DOI: https://doi.org/10.54216/IJNS.250309
    Iampan, A. Palanikumar, M. S., M. "Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set," International Journal of Neutrosophic Science, vol. , no. , pp. 92-105, 2025. DOI: https://doi.org/10.54216/IJNS.250309