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Fuzzy topological indices with application to cybercrime problem

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Abstract

The study of topological indices for fuzzy graphs is beneficial for fuzzy multi-criteria decision-making problems and various connected fuzzy networks. In this paper, we discuss two fuzzy topological indices, namely fuzzy Randic index and fuzzy harmonic index. We establish several upper bounds for these fuzzy indices. We also present the lower bounds of these indices for different fuzzy products, i.e., Cartesian product, cross product and lexicographic product. These results and bounds are established in terms of parameters, like number of nodes, edges, minimum and maximum vertex and edge membership, etc. We also present an algorithm to determine Randic index of vertices of fuzzy graph. Finally, we implement our model of fuzzy Randic index in cybercrime problem for detection of more active criminal who is involved in many crimes with other criminals.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Uzma Ahmad & Nasir Kaleem Khan

  2. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Arsham Borumand Saeid

Authors
  1. Uzma Ahmad
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  2. Nasir Kaleem Khan
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  3. Arsham Borumand Saeid
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Contributions

UA: concept, design, analysis, writing, or revision of the manuscript. NKK: concept, design, analysis, writing, or revision of the manuscript. ABS concept, design, analysis, writing, or revision of the manuscript.

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Correspondence to Arsham Borumand Saeid.

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Ahmad, U., Khan, N.K. & Saeid, A.B. Fuzzy topological indices with application to cybercrime problem. Granul. Comput. 8, 967–980 (2023). https://doi.org/10.1007/s41066-023-00365-2

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  • DOI: https://doi.org/10.1007/s41066-023-00365-2

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