Cluster-Centric Fuzzy Modeling

Abstract

In this study, we propose a cluster-oriented development of fuzzy models. An overall design process is focused on an efficient usage of fuzzy clustering, Fuzzy C-Means (FCM), in particular, to form information granules-clusters that are used in the construction of the fuzzy model. Fuzzy models are regarded as mappings from information granules expressed in the input and output spaces. This position motivates us to look at the development of the models through the perspective of the construction and efficient usage of information granules. This study directly associates fuzzy clustering with fuzzy modeling both in terms of conceptual and algorithmic linkages. The augmented FCM method is formed predominantly for modeling purposes so that a balance between the structural content present in the input and output spaces is achieved and this way the performance of the resulting fuzzy model is optimized. It is shown that the cluster-oriented modeling gives rise to the Mamdani-like fuzzy rules and a zero-order Takagi-Sugeno model (under a certain decoding scheme). We identify an interesting and direct linkage between the developed fuzzy models and a fundamental idea of encoding-decoding (or granulation-degranulation) encountered in processing fuzzy sets and Granular Computing, in general. Furthermore, refinements of zero-order fuzzy models are investigated leading to first-order fuzzy models with linear functions standing in the conclusions of the rules. A series of experiments is reported where we used synthetic and real-world data using which an issue of generalization capabilities is elaborated in detail.