Feature selection or Feature subset selection is a process of reducing the attribute space in the feature set. It is also stated that feature selection is a technique of identifying a subset of features. These subsets of features are selected by removing irrelevant or redundant features in the feature set. A good feature set is said to be that it contains highly correlated features with the cla...

We give a necessary condition for a set in Lp(Ω) spaces (1 < p <∞) to be self-extremal that partially extends our previous results to the case of Lp spaces. Examples of self-extremal sets in Lp(Ω) (1 < p <∞) are also given. In [4, 5], we introduced the notion of (self-) extremal sets of a Banach space (X ,‖ · ‖). For a nonempty bounded subset A of X , we denote by d(A) its diameter and by r(A) ...

Clustering is a process of grouping same objects into a specified number of clusters. K-means and Kmedoids algorithms are the most popular partitional clustering techniques for large data sets. However, they are sensitive to random selection of initial centroids and are fall into local optimal solution. K-means++ algorithm has good convergence rate than other algorithms. Distance metric is used...

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

A Chebyshev knot C(a, b, c, φ) is a knot which has a parametrization of the form x(t) = Ta(t); y(t) = Tb(t); z(t) = Tc(t + φ), where a, b, c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ ∈ R. We show that any two-bridge knot is a Chebyshev knot with a = 3 and also with a = 4. For every a, b, c integers (a = 3, 4 and a, b coprime), we describe an algorithm that gives all Cheb...

We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. In particular, we focus on states associated to vertices of a graph. call such vertex type states. Perfect between can be studied via Chebyshev polynomials. derive necessary condition eigenvalues graph for occur. addition, perfectly determine the complete multipartite graphs whose partite sets ...

We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N . This definition generalizes a very large class of Extended Complete Chebyshev systems in the one-dimensional case. This is the first of a series of papers in this area, which solves the longstanding problem of finding a satisfactory mul...

In this state-of-the-art paper, important advances that have been made during the past five years for both general and interval type-2 fuzzy sets and systems are described. Interest in type-2 subjects is worldwide and touches on a broad range of applications and many interesting theoretical topics. The main focus of this paper is on the theoretical topics, with descriptions of what they are, wh...