Universal fuzzy clustering model

Abstract

A universal fuzzy clustering model is proposed in order to adapt to the variability of a similarity data structure. For the purpose of the consideration of the variability of a similarity data, a nonlinear fuzzy clustering model has been proposed. In the nonlinear fuzzy clustering model, the similarity is represented by common degree of membership of a pair of objects to "each" fuzzy cluster and an ordinary aggregation operator is used for adjusting variety of the common degree of membership of a pair of objects to "each" fuzzy cluster. However, the ordinary aggregation operator is a binary operator and can only adjust for variety of common degree of membership of a pair of objects to "each" fuzzy cluster, it cannot adapt the variety of common degree of membership of a pair of objects to "all" fuzzy clusters. That is, this model cannot satisfactorily adjust to the variability of the obtained similarity data structure. Therefore, we define a new aggregation operator called a generalized aggregation operator in a linear product space spanned by "all" fuzzy clusters and propose a universal fuzzy clustering model based on this generalized aggregation operator in order to adjust to the variability of the obtained similarity data structure.