In this paper, we survey the relationship between the similarity measure and dissimilarity measure for fuzzy sets. First, we design a similarity measure using a distance measure for fuzzy sets and prove its usefulness. From this result, we assert that the similarity between two complementary fuzzy sets satisfies the fuzzy entropy definition. We also show that the summation of the similarity and...

A hypergraph is a generalization of graph in that the restriction pairwise affinity scores lifted favor can be evaluated between an arbitrary number inputs. Hypergraphs clustering process finding groups which members given exhibit high similarity and dissimilarity with outside their group. In this paper, we generalize well-known MapEquation, optimization equation used nonhypergraphs, for hyperg...

Many approaches to Music Information Retrieval tasks rely on correctly determining if two segments of a given musical recording are repeats of each other. Repetitions in recordings are rarely exact, and identifying the appropriate threshold for these pairwise decisions is crucial for tuning MIR algorithms. However, current approaches for determining and reporting this threshold parameter are de...

Although the “scale-free” literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a...

Although the “scale-free” literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a...