Information granulation as a basis of fuzzy modeling

Fuzzy clustering forms a cornerstone of fuzzy (granular) modeling. The clusters (prototypes) are viewed as a blueprint of the model that is further refined through a number of detailed estimation techniques. In this study, we claim that while clustering is indisputable essential to fuzzy modeling, the essence of clustering mechanisms supporting this process of information granulation is not compatible with the character of the task at hand. In modeling, the required constructs are inherently direction-sensitive (that is we clearly distinguish between input and output variables). On the other hand, fuzzy clustering is direction neutral and during the formation of the clusters does not take this into consideration. We re-formulate the clustering so that the directionality aspect can be addressed in the optimization process. This leads to a new, augmented objective function to be minimized. A detailed algorithm is derived. As the directional sensitivity of the clustering method gives rise to different numbers of clusters in the input and output space, it becomes necessary to identify a mapping between these clusters which in turn gives rise to some allocation problem. Because of its inherently combinatorial character, the proposed solution is obtained through some genetic optimization. Comprehensive experiments demonstrate the performance of the approach and compare it with some of the generic version of the FCM clustering.