Based on the axiom de nition of distance measure, some new formulas of fuzzy entropy induced by distance measure and some new properties of distance measure are given. A characterization of a -distance measure is a metric de ned on all fuzzy sets is obtained. c © 2001 Elsevier Science B.V. All rights reserved.

To each coherent configuration (scheme) C and positive integer m we associate a natural scheme Ĉ(m) on the m-fold Cartesian product of the point set of C having the same automorphism group as C. Using this construction we define and study two positive integers: the separability number s(C) and the Schurity number t(C) of C. It turns out that s(C) ≤ m iff C is uniquely determined up to isomorphi...

Consider a straight line on a flat surface running from point A to C and passing though B. Suppose the distance AB to be four inches, and the distance BC to be six inches. We can infer that the distance AC is ten inches. Of all geometrical inferences, this is surely one of the simplest. Of course, things are a little more complicated if the surface is not flat. If A, B and C are points on a sph...

Let G be a given connected graph on n vertices. Suppose N facilities are located in the vertices of the graph. We consider the expected distance between two randomly chosen facilities. This is modelled by the following definition: Let G be a connected graph and let each vertex have weight c(v). The average distance of G with respect to c is defined as µ c (G) = N 2 −1 {u,v}⊆V (G) d G (u, v), wh...

The population genetic structures of Culex pipiens Linnaeus were evaluated in China over a 2000 km transect that encompasses the two subspecies, C. p. pallens and C. p. quinquefasciatus. Four polymorphic allozyme loci were investigated in 1376 mosquitoes sampled from 20 populations across four provinces. These loci were not statistically dependent with no apparent heterozygote deficit or excess...

Given a collection C of partitions of a base set S, the NP-hard Consensus Clustering problem asks for a partition of S which has a total Mirkin distance of at most t to the partitions in C, where t is a nonnegative integer. We present a parameterized algorithm for Consensus Clustering with running time O(4.24 ·k+ |C| · |S|), where k := t/|C| is the average Mirkin distance of the solution partit...

Let C be a code over q of length n and distance d = d(C): The (Hamming) distance distribution of the code is an (n + 1)-vector (A0 = 1; A1; : : : ; An); where Aw = Aw(C) := (]C) 1jf(x; x0) 2 C : d(x; x0) = wgj: Of course Aw = 0 if 1 w d 1: Let fCng be a family of binary linear codes of growing length n and let dn = d(Cn): G. Kalai and N. Linial [2] conjectured that for any such family the numbe...

Let B,, denote the set of n-bit binary strings, and let Q, denote the graph of the n-cube where V(Q,> = B, and where two vertices are adjacent iff their Humming distance is exactly one. A subset C of B, is called a code, and the elements of C are referred to as codewords. C is said to be a linear code if the codeword obtained from component-wise sum (modulo 2) of any two elements of C is again ...

Relational clustering is an extension of clustering for relational data. Fuzzy c-Medoids (FCMdd) based linear fuzzy clustering extracts intrinsic local linear substructures from relational data. However this linear clustering was affected by noise or outliers because of using Euclidean distance. Alternative Fuzzy c-Means (AFCM) is an extension of Fuzzy c-means, in which a modified distance meas...

The paper proposes a computationally feasible method for measuring contextsensitive semantic distance between words. The distance is computed by adaptive scaling of a semantic space. In the semantic space, each word in the vocabulary V is represented by a multidimensional vector which is obtained from an English dictionary through a principal component analysis. Given a word set C which specifi...