Sparse representations using overcomplete dictionaries has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. The K-SVD algorithm is an iterati...

We establish some stability results concerning the general cubic functional equation f(x+ ky)− kf(x+ y) + kf(x− y)− f(x− ky) = 2k(k − 1)f(y) for fixed k ∈ N\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any ap...

Abstract— Sequential circuits are the important components of a computer system as they process binary data and buffers binary output for the next period.. Sequential circuits are the interconnection of logic gates and Flip Flops and the buffering of binary output for the next period is carried out by the Flip Flops by their inherent feedback mechanism. Sequential circuits basically process bin...

Many clustering methods have been proposed, including fuzzy k-means, which allows an object to be assigned to multi-clusters with different degree of membership. However, the memberships that result from fuzzy k-means, are rarely analyzed and visualized properly, but converted to 0-1 memberships. In this paper, we propose a new approach to visualize fuzzy-clustered data. The scheme provides a g...

Keywords--Fuzzy numbers, Convexity, Preinvexity, Generalized convexity, Fuzzy mappings. 1. I N T R O D U C T I O N Let R n deno te t he n -d imens iona l Euc l idean space. T h e suppor t , supp (p), of a fuzzy set # : R n ~ I = [0, 1] is def ined as s u p p ( # ) = { x e R n ] # ( x ) > 0} . A fuzzy set # : R n ~ I is cal led fuzzy convex if i t is quas i concave in c o m m o n sense on its su...

Medical image segmentation plays a vital role in image processing due to the catering needs of the medical images in automating, delineating anatomical structures and diagnosis. Very often the medical images contain uncertain, vague, and incomplete data definition. The concepts of lower and upper approximations of rough sets effectively handle this data. In this paper, rough sets based clusteri...

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...

In the real world, most criteria have inter-dependent or interactive characteristics so they cannot be evaluated by conventional additive measures. Thus, to approximate the human subjective evaluation process, it would be more suitable to apply a fuzzy integral model, in which it is not necessary to assume additivity and independence. This research proposes an effective algorithm to determine t...

Matrix descriptions of even dimensional fuzzy spherical branes S in Matrix Theory and other contexts in Type II superstring theory reveal, in the large N limit, higher dimensional geometries SO(2k+1)/U(k), which have an interesting spectrum of SO(2k+1) harmonics and can be up to 20 dimensional, while the spheres are restricted to be of dimension less than 10. In the case k = 2, the matrix descr...

This work introduces FINkNN, a k-nearest-neighbor classifier operating over the metric lattice of conventional interval-supported convex fuzzy sets. We show that for problems involving populations of measurements, data can be represented by fuzzy interval numbers (FINs) and we present an algorithm for constructing FINs from such populations. We then present a latticetheoretic metric distance be...