The notion of a fuzzy set, a natural extension of a classical set, was defined in 1965 by L.A. Zadeh; see [16]. Since that time, the fuzzy set theory has been deeply developed and it has influenced many fields of applications and therefore we can find results in branches like: fuzzy time series, fuzzy modeling, fuzzy graph theory and finally, the most often one fuzzy control. In general, the fu...

In this article we propose a direct adaptive fuzzy control method for MIMO nonlinear plant encountered mainly in robotics. The fuzzy adaptive law ensures the stability, convergence of the controlled outputs, and "boundedness" of adaptation parameters. In this method, the approximation error of the fuzzy logic system is estimated by an adaptive law independently of external disturbances. Moreove...

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 rough set theory usually is used in datamining. At this time, we will suppose the approximation operator to satisfy some wonderful properties. It need us to think about the basis algebra, the binary relation and the approximation operator’s form in the rough set model. Lfuzzy rough approximation operator is a general fuzzy rough approximation operator. Comparing with the others rough approx...

In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

We examine the properties of function approximation using polynomial rules in a fuzzy system. We show that this kind of fuzzy function approximation is equivalent to Lagrange polynomial interpolation between turning points when normalized fuzzy function memberships are used. The fuzzy inference procedure combines two polynomials of degree n and m in x into one single polynomial of at most degre...

Rough set theory can be generalized by induced topology through equivalence relations. Motivated the work of generalization rough via topology, concept and properties $ \tau-\mathfrak{K} $-fuzzy open (closed) sets are proposed. Considering sets, we have obtained lower upper approximations also proved their properties. represented as $-open \alpha level sets. The fuzzy on basis binary relation c...

The so-called measure of approximation quality plays an important role in many applications of rough set based data analysis. In this chapter, we provide an overview on various extensions of approximation quality based on rough-fuzzy and fuzzy-rough sets, along with highlighting their potential applications as well as future directions for research in the topic.

Two extensions of classical Shepard operators to the fuzzy case are presented. We study Shepard-type interpolation/approximation operators for functions with domain and range in the fuzzy number’s space and max-product approximation operators. Error estimates are obtained in terms of the modulus of continuity.

Most existing universal approximation results for fuzzy systems are based on the assumption that we use t conorms and t conorms to represent and and or Yager has proposed to use within the fuzzy system modeling paradigm more general operations based on uninorms In this paper we show that the universal approximation property holds for an arbitrary choice of a uninorm