Fuzzy Clustering Models and Their Related Concepts

Abstract

This chapter describes fuzzy clustering models. Fuzzy clustering models are typical examples of model-based clustering. The purpose of the model-based clustering is to obtain the optimal partition of objects by fitting the model to the observed similarity (or dissimilarity) of objects. The merit of model-based clustering is that we can obtain a mathematically clearer solution as the clustering result, because we know the mathematical features of the model. However, when we observe a large amount of complex data, it is difficult to fit the simple model to the data to obtain a useful result. In order to solve this problem, we have extended the model in the framework of fuzzy clustering models to adjust to the complexity caused from the recent variety of vast amounts of data. This chapter describes how we extend the fuzzy clustering models, along with the mathematical features of the several fuzzy clustering models. In particular, we describe the novel generalized aggregation operator defined on the product space of linear spaces and the generalized aggregation operator based nonlinear fuzzy clustering model.