It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry. Given a reflexive and symmetric fuzzy relation, the new algorithm computes a T-indistinguishability that is contained in the fuzzy relation. It has been developed a C++ program that generates random symmetric fuzzy relations or random symmetric and reflexive fuzzy relations and...

The distance measure is an important criterion in any clustering algorithm. This paper shows how fuzzy clustering results can be improved by introducing a weighting factor in the inter-objects distance measures. New weighted versions of four well-known distance measures are considered. These distances are tested, using the fuzzy c-means algorithm, on three datasets. Experimental results show th...

This paper proposes a classi"cation of fuzzy distances with respect to the requirements needed for applications in image processing under imprecision. We distinguish, on the one hand, distances that basically compare only the membership functions representing the concerned fuzzy objects, and, on the other hand, distances that combine spatial distance between objects and membership functions. To...

This paper focuses on the possible embedding of the uncertainty regarding the colors of an image into histogramtype descriptors. The uncertainty naturally arises from both the quantization of the color components and the human perception of colors. Fuzzy histograms measure the typicality of each color within the image. We define various fuzzy color histograms following a taxonomy that classifie...

For intuitionistic fuzzy sets, it is argued that three dimensional distance functions are not necessary because two dimensional distance functions already provide a simple and concise expression of the distance between two intuitionistic fuzzy sets. However, we show that a three dimensional interpretation of intuitionistic fuzzy sets could give different comparison results to the ones obtained ...

This paper presents adaptive and non-adaptive fuzzy c-means clustering methods for partitioning symbolic interval data. The proposed methods furnish a fuzzy partition and prototype for each cluster by optimizing an adequacy criterion based on suitable squared Euclidean distances between vectors of intervals. Moreover, various cluster interpretation tools are introduced. Experiments with real an...

Given a finite totally ordered set of linguistic terms, the operations intersection and connected union provide a lattice structure to the set of hesitant fuzzy linguistic term sets. In this framework, hesitant fuzzy linguistic descriptions of a given set of alternatives are considered. A distance between hesitant fuzzy linguistic descriptions is introduced based on the properties of the lattic...

Fuzzy measures and integrals have been used in multiple applications in the area of information fusion. They can be used to aggregate information when information sources are not independent. Fuzzy measures are used to represent our background knowledge on the information sources. In particular, they can be used to model the dependencies between the variables. One of the applications of Choquet...

A fuzzy approach is proposed here for restoring color images that are corrupted with additive noise. The proposed fuzzy approach consists of two sub-filters, where the first fuzzy sub-filter computes the fuzzy distances between the color components of the central pixel and its neighborhood using Gaussian combination membership function, and the second sub-filter corrects the pixels where color ...

We study additive distances and quasi-distances between words. We show that every additive distance is finite. We then prove that every additive quasi-distance is regularity-preserving, that is, the neighborhood of any radius of a regular language with respect to an additive quasi-distance is regular. Finally, similar results will be proven for context-free, computable and computably enumerable...