in this paper, we generalize fuzzy banach contraction theorem establishedby v. gregori and a. sapena [fuzzy sets and systems 125 (2002) 245-252]using notion of altering distance which was initiated by khan et al. [bull. austral.math. soc., 30(1984), 1-9] in metric spaces.

Several different metrics have been proposed to describe distance between intervals and, more generally, between compact sets. In this paper, we show that from the viewpoint of interval computations, the most adequate distance is the Hausdorff distance dH(A,A ′) – the smallest value ε > 0 for which every element a ∈ A is ε-close to some element a′ ∈ A′, and every element a′ ∈ A′ is ε-close to s...

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...

In this paper we investigate the Erdös/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been classically used to study this problem. We conjecture that a majorant for the spherical means suffices to prove the distance conjecture(s) in this setting. For a ...

A point set X in the Euclidean plane is called a k-distance set if there are exactly k different distances between distinct points in X. Let g(k) denote the maximum number of points in a k-distance set. For example, it is well known that g(1) = 3, realized by the three vertices of an equilateral triangle. Erdős and Fishburn [2] introduce the problem of determining g(k). To date only six values ...

A rational (resp. integral) distance set is a subset S of the plane R such that for all s, t ∈ S, the distance between s and t is a rational number (resp. is an integer). Huff [4] considered rational distance sets S of the following form: given distinct a, b ∈ Q∗, S contains the four points (0,±a) and (0,±b) on the y-axis, plus points (x, 0) on the x-axis, for some x ∈ Q∗. Such a point (x, 0) m...

A planar point-set X in Euclidean plane is called a k-distance set if there are exactly k different distances among the points in X. The function g(k) denotes the maximum number of points in the Euclidean plane that is a k-distance set. In 1996, Erdős and Fishburn conjectured that for k > 7, every g(k)-point subset of the plane that determines k different distances is similar to a subset of the...

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the...

A level set approach for computing solutions to incompressible two-phase ow. A viscosity solutions approach to shape-from-shading. SIAM. 19 Proof: Every simply connected shape has a simply connected skeleton 20]. Only circles have skeletons that are single points. Therefore, the skeletons of all other simply connected shapes have at least two end points. The proof follows immediately from Lemma...