Alice wants to prove that she is young enough to borrow money from her bank, without revealing her age. She therefore needs a tool for proving that a committed number lies in a specific interval. Up to now, such tools were either inefficient (too many bits to compute and to transmit) or inexact (i.e. proved membership to a much larger interval). This paper presents a new proof, which is both ef...

The interval number of a graph G, denoted i(G), is the least positive integer t for which G is the intersection graph of a family of sets each of which is the union of at most t cIosed intervals of the real line IR. Trotter and Harary showed that the interval number of the complete bipartite graph K(m, n) is [(mn + I)/(m + n)]. Matthews showed that the interval number of the complete multiparti...

The interval number i(P) of a poset P is the smallest t such that P is a containment of sets that are unions of at most t real intervals. For the special poset Bn(k) consisting of the singletons and ksubsets of an n-element set, ordered by inclusion, i(Bn(k)) = min {k, n − k + 1} if |n/2 − k | ≥ n/2 − (n/2). For bipartite posets with n elements or n minimal elements, i(P) ≤  n lgn − lglgn  + ...

this paper proposes an alternative approach for efficiency analysis when a set of dmus uses interval scale variables in the productive process. to test the influence of these variables, we present a general approach of deriving dea models to deal with the variables. we investigate a number of performance measures with unrestricted-in-sign interval and/or interval scale variables.

A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring where each vertex is assigned a color from {1, . . . , k}. A list assignment to G is an assignment L = {L(v)}v∈V (G) of lists of colors to the...

* Correspondence author. Abstract The fuzzy multi-attribute decision making problems are investigated, in which the attribute values are given as intervalvalued intuitionistic fuzzy numbers and the attribute weight information is incomplete. Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers...

Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical interval...