Constructing fuzzy measures: a new method and its application to cluster analysis

We first prove that for a given set of data there exists a fuzzy measure fitting exactly the data if and only if there exists an exact solution of the associated fuzzy relation equation. Secondly, we continue to study the special neural network we proposed in Proc. IFSA'95 World Congress, pp. 61-64 (1995), and describe a learning algorithm for obtaining an approximate fuzzy measure when no one exactly fits the data. Finally, we propose a clustering method based on fuzzy measures and integrals. A benchmark data set, the well-known Iris data set, is adopted to illustrate the method.