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t-Norm Fuzzy Graphs

Author

Listed:
  • John N. Mordeson

    (Department of Mathematics, Creighton University, Omaha, NE 68178, USA)

  • Sunil Mathew

    (Department of Mathematics, National Institute of Technology Calicut, Kozhikode 673601, Kerala, India)

Abstract

We generalize the definition of a fuzzy graph by replacing minimum in the basic definitions with an arbitrary t-norm. The reason for this is that some applications are better modeled with a t-norm other than minimum. We develop a measure on the susceptibility of trafficking in persons for networks by using a t-norm other than minimum. We also develop a connectivity index for a fuzzy network. In one application, a high connectivity index means a high susceptibility to trafficking. In the other application, we use a method called the eccentricity of an origin country to determine the susceptibility of a network to trafficking in persons. The models rest on the vulnerabilities and the government responses of countries to trafficking.

Suggested Citation

  • John N. Mordeson & Sunil Mathew, 2018. "t-Norm Fuzzy Graphs," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 129-143, March.
    • Handle: RePEc:wsi:nmncxx:v:14:y:2018:i:01:n:s1793005718500096
    DOI: 10.1142/S1793005718500096
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    Citations

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    Cited by:

    1. John N. Mordeson & Sunil Mathew & Santanu Acharjee, 2018. "Aggregation Operators: Applications to Human Trafficking and Slavery," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 403-421, November.
    2. John N. Mordeson & Sunil Mathew, 2018. "t-Norm Fuzzy Incidence Graphs," Mathematics, MDPI, vol. 6(4), pages 1-12, April.
    3. John N. Mordeson & Sunil Mathew & Davender S. Malik, 2018. "Generalized Fuzzy Relations," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 187-202, July.
    4. Shanookha Ali & Sunil Mathew & John N. Mordeson & Hossein Rashmanlou, 2018. "Vertex Connectivity of Fuzzy Graphs with Applications to Human Trafficking," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 457-485, November.

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