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 2 , PP: 283-292, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management

A. Manshath 1 * , K. Rajesh 2 , M. Logeshwari 3 , R. Saranya 4

  • 1 Department of Mathematics Actuarial Science, B.S. Abdur Rahman Institute of Science and Technology, Chennai – 600048, Tamil Nadu, India - (ameer.manshath@gmail.com)
  • 2 Department of Mathematics, Government Arts and Science College for Women, Krishnagiri, Tamil Nadu – 635104, India. - (rajeshagm@gmail.com)
  • 3 Department of Mathematics, Sathyabama Institute of Science and Technology (Deemed to be University), Chennai – 600119, Tamil Nadu, India. - (logeshjimail@gmail.com)
  • 4 Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore – 641202, Tamil Nadu, India. - (sinesaranya@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.240225

    Received: November 21, 2023 Revised: February 08, 2024 Accepted: May 07, 2024
    Abstract

    we are introducing the model-type operators over Interval-Valued Fuzzy Neutrosophic Sets with time moments [IVFNS] and learn a few of their properties with numerical examples to demonstrate the defined operations and operators. Also introduce various distance measures over the extension of interval neutrosophic sets as well as apply the introduced measures in ecological management in this direct to decide the type of corrosion disturbing some towns for valuable management to be taken, using this normalized distance measures. The extensions of neutrosophic connection values and non-connection values be not used for all time probable positive to our fulfillment, but this concept IVTNFS part has more significant responsibility at this point since the time progress with IVN-fuzzy sets provide the accurate solution in factual situations similarly, conclusion making, career deciding and so on. This is the main reason for taking in the extensions of neutrosophic sets.

    Keywords :

    Intuitionistic Fuzzy Sets (IFS) , Temporal Intuitionistic Fuzzy Sets (TIFS) , Neutrosophic Set , Interval Valued Neutrosophic Set , Interval Valued Intuitionistic Fuzzy Sets (IVIFS) and Interval Valued Temporal Neutrosophic Fuzzy Sets (IVTNFS).

    References

     

    [1]                Adamu, I.M., Application of intuitionistic fuzzy sets to environmental management. Notes on Intuitionistic Fuzzy Sets, 27(3), 40–50, 2021.

    [2]                Atanassov, K. T., Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87 – 96, 1986.

    [3]                Atanassov, K. T., Intuitionistic Fuzzy Sets - Theory and Applications. Springer Verlag, New York, 1999.

    [4]                Atanassov, K.T., Szmidt, E.,&Kacprzyk, J., Shrinking Operators over Interval Valued Intuitionistic Fuzzy Sets. Notes on Intuitionistic Fuzzy Sets,24(4), 20 – 28, 2018.

    [5]                Atanassov, K. T.,&Gargov, G., Interval–Valued Fuzzy Sets. Fuzzy Sets and Systems, 31,343 – 349, 1989.

    [6]                Atanassov, K.T., Temporal intuitionistic fuzzy sets. Comptes Rendusdel’ AcademieBulgare, 7,5 – 7, 1991.

    [7]                Anand, M.C. J., & Bharatraj, J., Interval-Valued Neutrosophic Numbers with WASPAS. In: Kahraman, C., Otay, İ. (eds) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Studies in Fuzziness and Soft Computing, Springer, Cham, 435-453, 2019.

    [8]                Kumar, D. S., Biswas, R.,& Roy, A, R., Some operations on intuitionistic fuzzy sets. Fuzzy Sets and Systems,114(3), 477 – 484, 2000.

    [9]                Smarandache, F., &Broumi, S., New Distance and Similarity Measures of Interval Neutrosophic Sets. Neutrosophic Theory and Its Applications, at 17th International Conference on Information Fusion, Salamanca, Spain, 7-10,2014.

    [10]              Parvathi, R., & Geetha, S.P., A note on properties of temporal intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 15(1),42–48, 2009.

    [11]              Rajesh. K., &Srinivasan, R., A Note on Properties of Temporal Intuitionistic Fuzzy Sets of Second Type.International Journal of Multidisciplinary Research and Modern Education, 2(2), 378 – 383, 2016.

    [12]              Rajesh, K., Distance between Temporal Intuitionistic Fuzzy Sets of Second Type. International Journals of Advances Science and Engineering, 6(3), 1445 – 1448, 2019.

    [13]              Rajesh, K., Certain Level Operators over Temporal Intuitionistic Fuzzy Sets. International Journals of Advances Science and Engineering, 9(2),2805-2809, 2022.

    [14]              Rajesh, K., &Rathod. S., at al, A study on Interval Valued Temporal Neutrosophic Fuzzy Sets. International Journals of Neutrosophic Science,23(1),341 – 349, 2024.

    [15]              Yilmaz, S., &Cuvalcioglu, G., On level operators for temporal Intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets,20(2),6 – 15, 2014.

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

    [17]              Smarandache. F., Deli,I.,& Ali, M., Bipolar neutrosophic sets and their application based on multi-criteria decision-making problems. In: Proceedings of the 2015 international conference on advanced mechatronic systems (ICAMechS). IEEE, Beijing, 249–254, 2015.

    [18]              Smarandache, F., Zhang, Y. Q., Sunderraman,R.,& Wang, H., Single valued neutrosophic sets. MultispaceMultistruct, 4, 410-413, 2010.

    [19]              Broumi, S.,& Smarandache, F., Several Similarity Measures of Neutrosophic Sets. Neutrosophic Sets and Systems, 1,54-62, 2013.

    [20]              Das, S., Roy, B., Kar, M. B., &Samarjit, Neutrosophic fuzzy set and its application. Journal of Ambient Intelligence and Humanized Computing, 1-13, 2020.

    [21]              Turksen, I. B., Interval-valued fuzzy sets based on normal forms.Fuzzy Sets and Systems, 20(2), 191 – 210, 1986.

    [22]              Wang, H., Smarandache, F.,Zhang, Y. Q., &Sunderraman, R., Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis, Phoenix, Ariz, USA, 2005.

    [23]              Chen, X., Zhang, H., &Wang, J., “Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems”, The Scientific World Journal, pp. 1-15, 2014.

    [24]              Xu &Zeshui, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision, 22(2),215 – 219, 2007.

    [25]              Zhang, Z., Interval Valued Intuitionistic Hesitancy Fuzzy aggregation operators and their application in group decision-making. Journals of applied mathematics, 33, 1 – 25, 2013.

    [26]              Zadeh, L. A., Fuzzy sets. Information and Control,8(15), 338 – 353, 1965.

    Cite This Article As :
    Manshath, A.. , Rajesh, K.. , Logeshwari, M.. , Saranya, R.. Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 283-292. DOI: https://doi.org/10.54216/IJNS.240225
    Manshath, A. Rajesh, K. Logeshwari, M. Saranya, R. (2024). Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management. International Journal of Neutrosophic Science, (), 283-292. DOI: https://doi.org/10.54216/IJNS.240225
    Manshath, A.. Rajesh, K.. Logeshwari, M.. Saranya, R.. Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management. International Journal of Neutrosophic Science , no. (2024): 283-292. DOI: https://doi.org/10.54216/IJNS.240225
    Manshath, A. , Rajesh, K. , Logeshwari, M. , Saranya, R. (2024) . Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management. International Journal of Neutrosophic Science , () , 283-292 . DOI: https://doi.org/10.54216/IJNS.240225
    Manshath A. , Rajesh K. , Logeshwari M. , Saranya R. [2024]. Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management. International Journal of Neutrosophic Science. (): 283-292. DOI: https://doi.org/10.54216/IJNS.240225
    Manshath, A. Rajesh, K. Logeshwari, M. Saranya, R. "Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management," International Journal of Neutrosophic Science, vol. , no. , pp. 283-292, 2024. DOI: https://doi.org/10.54216/IJNS.240225