The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutual information of fuzzy partitions and for Kullback-Leibler divergence with respect to fuzzy P-measures are established. In addition, a convexity o...

Cluster validity indices have been used to evaluate the quality of fuzzy partitions. In this paper, we propose a new index, which uses concepts of Fuzzy Rough sets to evaluate the average intra-cluster similarity of fuzzy clusters produced by the fuzzy c-means algorithm. Experimental results show that contrasted with several well-known cluster validity indices, the proposed index can yield more...

Since the proposal of Zadeh and Mamdani’s seminal ideas, interpretability is acknowledged as one of the most appreciated and valuable characteristics of fuzzy system identification methodologies. It represents the ability of fuzzy systems to formalize the behavior of a real system in a human understandable way. Interpretability analysis involves two main points of view: readability of the knowl...

This work studies a new distance function which takes into account expert knowledge by making use of fuzzy partitions. It considers the symbolic distances between concepts and is equivalent to the Euclidean distance for regular partitions made of triangular membership functions. Its behaviour is investigated in comparison with that of the Euclidean distance and its interest is shown for cluster...

In this paper, we investigate the indirect adaptive regulation problem of unknown affine in the control nonlinear systems. The proposed approach consists of choosing an appropriate system approximation model and a proper control law, which will regulate the system under the certainty equivalence principle. The main difference from other relevant works of the literature lies in the proposal of a...

Random projection is a popular method for dimensionality reduction due to its simplicity and efficiency. In the past few years, random projection and fuzzy c-means based cluster ensemble approaches have been developed for high dimensional data clustering. However, they require large amounts of space for storing a big affinity matrix, and incur large computation time while clustering in this aff...

The Rand index is a measure commonly used to compare crisp partitions. Campello (2007) and Hüllermeier and Rifqi (2009) respectively, proposed two extensions of this index capable to compare fuzzy partitions. These approaches are useful when continuous values of attributes are discretized using fuzzy sets. In previous works we experimented with these extensions and compared their accuracy with ...