Probabilistic clustering algorithms for fuzzy rules decomposition

The fuzzy c-means (FCM) clustering algorithm is the best known and used method in fuzzy clustering and is generally applied to well defined set of data. In this paper a generalized Probabilistic fuzzy c-means (FCM) algorithm is proposed and applied to clustering fuzzy sets. This technique leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of a flat fuzzy system results a set of decomposed sub-systems that will be conveniently linked into a Parallel Collaborative Structures

Probabilistic fuzzy clustering algorithm for fuzzy rules decomposition

The Fuzzy C-Means (FCM) clustering algorithm is the best known and the most used method for fuzzy clustering and is generally applied to well defined sets of data. In this work a generalized Probabilistic Fuzzy C-Means (PFCM) algorithm is proposed and applied to fuzzy sets clustering. The methodology presented leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of a flat fuzzy system the result is a set of decomposed sub-systems that will be conveniently linked into a Parallel Collaborative Structure.This work was supported by Fundação para a Ciência e Tecnologia (FCT) under grant POSI/SRI/41975/2001 and CITAB (UTAD)

Clustering of TS-fuzzy system

This paper presents a fuzzy c-means clustering method for partitioning symbolic interval data, namely the T-S fuzzy rules. The proposed method furnish a fuzzy partition and prototype for each cluster by optimizing an adequacy criterion based on suitable squared Euclidean distances between vectors of intervals. This methodology leads to a fuzzy partition of the TS-fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of TS-fuzzy system the result is a set of additive decomposed TS-fuzzy sub-systems. In this work a generalized Probabilistic Fuzzy C-Means algorithm is proposed and applied to TS-Fuzzy System clustering

Possibilistic clustering for shape recognition

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise

Decomposition of a greenhouse TS-Fuzzy model by clustering process

This paper presents a fuzzy c-means clustering method for decompose a T-S fuzzy system. This technique is used to organize the fuzzy greenhouse climate model into a new structure more interpretable, as in the case of the physical model. This new methodology was tested to split the inside greenhouse air temperature and humidity flat fuzzy models into fuzzy sub-models. These fuzzy sub-models are compared with its counterpart’s physical sub-models. This algorithm is applied to the T-S fuzzy rules. The results are several clusters of rules where each cluster is a new fuzzy sub-system. This is a generalized Probabilistic Fuzzy C-Means (PFCM) algorithm applied to TS-Fuzzy System clustering. This allows automatic organization of one fuzzy system into a multimodel Hierarchical Structure.This work was supported by Fundação para a Ciência e Tecnologia (FCT) under grant POSI/SRI/41975/2001 and by CITAB - Centro de Investigação e Tecnologias Agro-Abientais e Biológicas

Self-Learning Fuzzy Spiking Neural Network as a Nonlinear Pulse-Position Threshold Detection Dynamic System Based on Second-Order Critically Damped Response Units

Architecture and learning algorithm of self-learning spiking neural network in fuzzy clustering task are outlined. Fuzzy receptive neurons for pulse-position transformation of input data are considered. It is proposed to treat a spiking neural network in terms of classical automatic control theory apparatus based on the Laplace transform. It is shown that synapse functioning can be easily modeled by a second order damped response unit. Spiking neuron soma is presented as a threshold detection unit. Thus, the proposed fuzzy spiking neural network is an analog-digital nonlinear pulse-position dynamic system. It is demonstrated how fuzzy probabilistic and possibilistic clustering approaches can be implemented on the base of the presented spiking neural network