Abstract
We define closure operator on the set of fuzzy relations on S and show that the closed hull of a fuzzy relation ( S, μ) is given by Γ( S, μ) = ( S, μ σ μ ). We define strong fuzzy relation and derive some results to investigate the relationship between closed, strong, and symmetric fuzzy relations. We give a counterexample to show that the composition of two closed fuzzy relations need not be a closed fuzzy relation. We also give a much simpler proof of Theorem 4.2 of Bhattacharya and Mukherjee and provide counterexamples to show that their Lemma 3.4 and Theorem 3.1 of Das do not always remain true.
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