Resum In many data mining processes, neighborhood operators play an important role as they are generalizations of equivalence classes which were used in the original rough set model of Pawlak. In this article, we introduce the notion of fuzzy neighborhood system of an object based on a given fuzzy covering, as well as the notion of the fuzzy minimal and maximal descriptions of an object. Moreov...

The covering radius problem has been considered by many authors (e.g. [ 1, 5, 61). Finally, let t(n, k) be the minimum possible covering radius for an (n, k) code and k(n, p) the minimum possible dimension of a code with covering radius p. The study of t(n, k) was initiated by Karpovsky. For a survey of these questions, see ]41. The main goal of this paper is to find good linear coverings. The ...

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed component f , and a variable component b that is proportional to the field-of-view area. When only one type of sensor or, in general, one type of disc, is availa...

A number of upper and lower bounds are obtained for K( n, R), the minimal number of codewords in any binary code of length n and covering radius R. Several new constructions are used to derive the upper bounds, including an amalgamated direct sum construction for nonlinear codes. This construction works best when applied to normal codes, and we give some new and stronger conditions which imply ...

Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. Frobenius number of this N-tuple is defined to be the largest positive integer that cannot be expressed as P N i=1 aixi where x1, ..., xN are non-negative integers. The condition that gcd(a1 , ..., aN ) = 1 implies that such number exists. The general problem of determining the Frobenius number given N and a1, ..., aN is NP-har...

We give an explicit upper bound of the minimal number of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in R, n > 2.

We will be considering sets of n-tuples over an alphabet A, in two important cases: A ¡ ¢ 0£ 1¤ (binary code); n¤ , all entries of each word distinct (set of permutations). We often impose closure conditions on these sets, as follows: A binary code is linear if it is closed under coordinatewise addition mod 2. A set of permutations is a group if it is closed under composition. x£ yïs the number...

Sol& P., A. Ghafoor and S.A. Sheikh, The covering radius of Hadamard codes in odd graphs, Discrete Applied Mathe-atics 37/38 (1992) 501-5 10. The use of odd graphs has been proposed as fault-tolerant interconnection networks. The following problem originated in their design: what is the graphical covering radius of an Hadamard code of length 2k1 and siLe 2k1 in the odd graph Ok? Of particular i...

The purpose of this paper is to discuss some recent generalizations of the basic covering radius problem in coding theory. In particular we discuss multiple coverings, multiple coverings of the farthest-o points and weighted coverings.

On the way of generalizing recent results by Cock and the second author, it is shown that when the basis q is odd, BCH codes can be lengthened to obtain new codes with covering radius R = 2. These constructions (together with a lengthening construction by the first author) give new infinite families of linear covering codes with codimension r = 2k + 1 (the case q = 3, r = 4k + 1 was considered ...