The notion of fuzzy is context dependent, so for each context very often there is a fuzzy theory. Present papers use the notion of neighborhood systems to unify them. A neighborhood system is an association that assigns to each datum a list of data (a neighborhood). Rough sets and topological spaces are special cases. A “real world” fuzzy set should allow small amount of perturbation, so it sho...

Methods like DBSCAN are widely used in the analysis of spatial data. These methods are based on the neighborhood relations which use distance between points. However, these neighborhood relations consider to have at least a certain number of neighbors within a definite boundary. In this proposed work such a neighborhood analysis is done by using the benefits of fuzzy sets theory. Usage of fuzzy...

In this paper, an adaptive fuzzy control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the control gains.Based on the backstepping technique, the adaptive fuzzy controller is constructed. The main contributions of the paper...

In this paper, we investigate the L-fuzzy proximities and the relationships betweenL-fuzzy topologies, L-fuzzy topogenous order and L-fuzzy uniformity. First, we show that the category of-fuzzy topological spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a coreective full subcategory. Second, we show that the category of L -fuzzy proximity spaces is isomorphic to the ...

In this paper, an adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time delays and unmeasured states. By using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed for estimating the unmeasured states. By combining the adaptive backstepping technique with adaptive fuzzy control desi...

What is granular computing? As we have said in [6]: There are no mathematically valid formal definitions yet. Informally, any computing theory/technology that involves elements and granules (generalized subsets) may be called granular computing (GrC). Intuitively, elements are the data, and granules are the basic knowledge. So granular computing includes data and knowledge computing/engineering...

A set-theoretic framework is proposed for granular computing. Each element of a universe is associated with a nonempty family of neighborhoods. A neighborhood of an element consists of those elements that are drawn towards that element by indistinguishability, similarity, proximity, or functionality. It is a granule containing the element. A neighborhood system is a family of granules, which is...