Results on t-Fuzzy Graphs

R. A. Borzooei, B. Sheikh Hoseini () and M. Mohseni Takallo ()
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R. A. Borzooei: Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran
B. Sheikh Hoseini: Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran
M. Mohseni Takallo: Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran

New Mathematics and Natural Computation (NMNC), 2020, vol. 16, issue 01, 143-161

Abstract: It is much more practical to use the t-norm than the minimum in defining the fuzzy graph. Hence, the concept of t-fuzzy graph was introduced by Mordeson et al. in [J. N. Mordeson and S. Mathew, t-norm Fuzzy Graphs, New Mathematics and Natural Computation 14(1) (2018) 129–143]. In this paper, we concentrate on the relatively new concept of fuzzy adjacency matrix of that t-fuzzy graphs. The purpose of this paper is to further develop a product of this fuzzy adjacency matrix based on t-fuzzy graphs. Moreover, two kinds of Boolean matrix are defined and relation between Normal Boolean matrix, product of adjacency matrix and 1-level cut Boolean matrix is obtained.

Keywords: Fuzzy graph; t-fuzzy graph; adjacency matrix; product of adjacency matrix; nilpotent t-norm; normal cycle; Boolean matrix (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S179300572050009X

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