The paper develops a clustering model of multi-criteria object evaluations, taking into account the reliability results obtained. Clustering is based on system fuzzy reference requirements about importance evaluated characteristics objects for each clusters. Object evaluations are formalized basis linguistic Z-numbers, both numbers which values variables. Information and cluster presented as se...

In this paper we investigate some relations between Bernstein polynomials and q-Euler numbers with weak weight α. From these relations, we derive some interesting identities on the q-Euler numbers with weak weight α. Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of p-adic rati...

Given a subset D of positive integers, an integer distance graph is a graphG(Z, D) with the set Z of integers as vertex set and with an edge joining two vertices u and v if and only if |u−v| ∈ D. In this paper we consider the problem of determining the chromatic number of certain integer distance graphs G(Z, D)whose distance set D is either 1) a set of (n + 1) positive integers for which the n ...

The Binet formula gives a natural way for Fibonacci numbers to be viewed as a function of a complex variable. We experimentally study the complex dynamics of the Fibonacci numbers viewed in that manner. Attracting and repelling fixed points are related to the filled Julia set and to regions of escape time images with fascinating behavior. Introduction The Fibonacci numbers are traditionally des...

following our previous presentation of a new three-fold symmetry for derivation of the magic numbers of nuclei based upon a quark state model of nuclei, here the nuclear binding energy is obtained from such new perspective. from this point of view, since each nucleon is made of three quarks, the binding energy of nuclei contains a volume term proportional to 3a (a is mass number). by considerin...

In this paper we consider two functionals of the Fekete–Szegö type: Φ f (μ)=a 2 a 4 -μa 3 and Θ for analytic functions f(z)=z+a z +a +..., z∈Δ, (Δ={z∈ℂ:|z|<1}) real numbers μ. For which is univalent convex in direction imaginary axis, find sharp bounds (μ) (μ). It possible to transfer results onto class

We use the following convention: X, x, y, z are sets and n, m, k, k, d are natural numbers. The following two propositions are true: (1) For all real numbers x, y such that x < y there exists a real number z such that x < z and z < y. (2) For all real numbers x, y there exists a real number z such that x < z and y < z. The scheme FrSet 1 2 deals with a non empty set A, a non empty set B, a bina...

A real number x is said to be eeective if there exists an algorithm which, given a required tolerance " 2 Z 2 Z , returns a binary approximation x ~ 2 Z 2 Z for x with jx ~ ? xj < ". In this paper, we review several techniques for computations with such numbers, and we will present some new ones.