An architecture for the implementation of possibilistic models in an object-oriented programming environment (C++ in particular) is described. Fundamental classes for special and general random sets, their associated fuzzy measures, special and general distributions and fuzzy sets, and possibilistic processes are speciied. Supplementary methods|including the fast MM obius transform, the maximum...

In medical imaging uncertainty is widely present in data, because of the noise in acquisition and of the partial volume effects originating from the low resolution of sensors. In particular, borders between tissues are not exactly defined and memberships in the boundary regions are intrinsically fuzzy. Therefore, computer assisted unsupervised fuzzy clustering methods turn out to be particularl...

Fuzzy c-means (FCM) clustering is based on minimizing the fuzzy within cluster scatter matrix trace but FCM neglects the between cluster scatter matrix trace that controls the distances between the class centroids. Based on the principle of cluster centers separation, fuzzy cluster centers separation (FCCS) clustering is an extended fuzzy c-means (FCM) clustering algorithm. FCCS attaches import...

General automata are considered with respect to normal-ization over semirings. Possibilistic automata are deened as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochas-tic automata where stochastic (+=) semirings are replaced by possi-bilistic (_=^) semirings; but where stochastic automata must be normal, fuzzy automata may be (resulting in possibilistic automata)...

In this paper, application of possibilistic clustering techniques to identification of local linear models will be discussed. In particular, a generalisation of some possibilistic algorithms in the bibliography is obtained. With the presented procedures, a trade-off between an “expected shape” of the membership functions and model fit can be stated. Possibilistic clustering may allow for better...

In some complicated datasets, due to the presence of noisy data points and outliers, cluster validity indices can give conflicting results in determining optimal number clusters. This paper presents a new index for fuzzy-possibilistic c-means clustering called Fuzzy-Possibilistic)FP (index, which works well clusters that vary shape density. Moreover, FPCM like most algorithms is susceptible ini...

A quality of centroid-based clustering is highly dependent on initialization. In the article we propose initialization based on the probability of finding objects, which could represent individual clusters. We present results of experiments which compare the quality of clustering obtained by k-means algorithm and by selected methods for fuzzy clustering: FCM (fuzzy c-means), PCA (possibilistic ...

We explore an approach to possibilistic fuzzy c-means clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical. Our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters, so that they are forced away from each other....

Probabilistic clustering techniques use the concept of memberships to describe the degree by which a vector belongs to a cluster. The use of memberships provides probabilistic methods with more realistic clustering than “hard” techniques. However, fuzzy schemes (like the Fuzzy c Means algorithm, FCW are open sensitive to outliers. We review four existing algorithms, devised to reduce this sensi...