In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough sets and rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a class of revised...

Spatial relations play important role in computer vision, scene analysis, geographic information systems (GIS) and content based image retrieval. Analyzing spatial relations by Force histogram was introduced by Miyajima et al [10] and largely developed by Matsakis [12] who used a quantitative representation of relative position between 2D objects. Fuzzy Allen relations are used to define the fu...

This paper discusses the generalization capability of neural networks based on various fuzzy operators introduced earlier by the authors as Fuzzy Flip-Flop based Neural Networks (FNNs), in comparison with standard (e.g. tansig function based, MATLAB Neural Network Toolbox type) networks in the frame of simple function approximation problems. Various fuzzy neurons, one of them based on a pair of...

Ordered fuzzy numbers that make possible to deal with fuzzy inputs quantitatively, exactly in the same way as with real numbers, are defined together with four algebraic operations. For defuzzyfication operators that play the main role when dealing with fuzzy controllers and fuzzy inference systems an approximation formula is given. In order to determine it when a training set is given a dedica...

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341–356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2–3) (1990) 191–209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough...

Ever since the first hybrid fuzzy rough set model was proposed in the early 1990’s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operati...

The paper discusses the generalization capability of two hidden layer neural networks based on various fuzzy operators introduced earlier by the authors as Fuzzy Flip-Flop based Neural Networks (FNNs), in comparison with standard networks tansig function based, MATLAB Neural Network Toolbox in the frame of a simple function approximation problem. Various fuzzy neurons, one of them based on new ...