Some properties of the fuzzy equivalence matrices

In fuzzy clustering, we always use fuzzy equivalence matrix to find the clustering results. Although fuzzy equivalence matrix is one of the most important tools in fuzzy clustering, it's hard to judge whether a fuzzy matrix is a fuzzy equivalence matrix directly. In this paper, some simple and useful properties of the fuzzy equivalence matrices have been proposed based on the basic properties proposed in the classical articles. Using these properties, the judgment whether a fuzzy matrix is a fuzzy equivalence matrix may become an easy work.