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Inverse Fuzzy Graphs with Applications

Author

Listed:
  • R. A. Borzooei

    (Department of Mathematics, Shahid Beheshti University, Tehran, Iran)

  • R. Almallah

    (Department of Mathematics, Shahid Beheshti University, Tehran, Iran)

  • Y. B. Jun

    (Department of Mathematics, Shahid Beheshti University, Tehran, Iran†Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea)

  • H. Ghaznavi

    (#x2021;Cellular and Molecular Research Center, Zahedan University of Medical Sciences, Zahedan, Iran)

Abstract

Rosenfeld [A. Rosenfeld, Fuzzy Graphs, Fuzzy Sets and Their Applications, eds. L. A. Zadeh, K. S. Fu and M. Shimura (Academic Press, New York, 1975), pp. 77–95.] defined the fuzzy relations on the fuzzy sets and developed the structure of fuzzy graph, as a graph with a membership degree (between zero and one) for the vertices and edges such that the membership degree of every edge is less than or equal to the minimum of the membership degree of its endpoints. Although this model of graph has many applications in the real life, it fails to solve a lot of problems, which we can use graph for its representation. This paper aimed to demonstrate a new type of graph with a membership degree (between zero and one) for the vertices and edges so that the membership degree of every edge becomes more than or equals the minimum of the membership degrees of its endpoints. This new type of graph is called inverse fuzzy graph “or” I-fuzzy graph, which can play a role in solving many problems which are not solved by fuzzy graph.

Suggested Citation

  • R. A. Borzooei & R. Almallah & Y. B. Jun & H. Ghaznavi, 2020. "Inverse Fuzzy Graphs with Applications," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 397-418, July.
    • Handle: RePEc:wsi:nmncxx:v:16:y:2020:i:02:n:s1793005720500246
    DOI: 10.1142/S1793005720500246
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