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Generalized Fuzzy Relations

Author

Listed:
  • John N. Mordeson

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

  • Sunil Mathew

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

  • Davender S. Malik

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

Abstract

Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld’s relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations. In this paper, we generalize fuzzy relations using arbitrary t-norms and t-conorms. Many of the results do not hold when minimum and maximum are replaced by an arbitrary norm and an arbitrary conorm. Reflexive, symmetric and transitive generalized fuzzy relations are also discussed and an application to human trafficking and illegal immigration is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:nmncxx:v:14:y:2018:i:02:n:s1793005718500126
    DOI: 10.1142/S1793005718500126
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    References listed on IDEAS

    as
    1. E. Darabian & R. A. Borzooei, 2018. "Results on Vague Graphs with Applications in Human Trafficking," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 37-52, March.
    2. John N. Mordeson & Sunil Mathew, 2017. "Human Trafficking: Source, Transit, Destination Designations," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 209-218, November.
    3. 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.
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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 & R. A. Borzooei, 2018. "Vulnerability and Government Response to Human Trafficking: Vague Fuzzy Incidence Graphs," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 203-219, July.
    3. 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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