The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...

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 ...

Orthogonal Tensor Neighborhood Preserving Embedding (OTNPE) is an efficient dimensionality reduction algorithm for two-dimensional images. However, insufficiencies of the robustness performance and deficiencies of supervised discriminant information are remained. Motivated by the sparse learning, an algorithm called Orthogonal Tensor Sparse Neighborhood Embedding (OTSNPE) for two-dimensional im...

Inference mechanisms and interpretations of fuzzy rule bases are studied together from the point of view of systems of fuzzy relation equations. A proper use of an inference mechanism connected to a fuzzy relation interpreting a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations which are motiva...

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

Min-implication fuzzy relation equations based on Booleantype implications can also be viewed as a way of implementing fuzzy associative memories with perfect recall. In this paper, fuzzy associative memories with perfect recall are constructed, and new on-line learning algorithms adapting the weights of its interconnections are incorporated into this neural network when the solution set of the...