In complex network analysis, fuzzy community detection is a challenging task that aims to reveal the network structure by assigning each vertex quantitative membership-degrees to various communities. In this paper, we propose a fuzzy community detection method that iteratively propagates membership-degrees of all vertices. In each iteration, a candidate seed vertex of a potential community is f...

This paper presents a novel learning algorithm of fuzzy perceptron neural networks (FPNNs) for classifiers that utilize expert knowledge represented by fuzzy IF-THEN rules as well as numerical data as inputs. The conventional linear perceptron network is extended to a second-order one, which is much more flexible for defining a discriminant function. In order to handle fuzzy numbers in neural n...

A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a colored graph lacks colorful cycles iff it is Gallai, i.e., lacks colorful triangles. We then show that, under the operation m◦n ≡ m+n−2, the omitted lengths of colorful cycles in a colored graph form a monoid isomorp...