in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

The theoretical background for abstract formalization of the vague phenomenon of complex systems is the fuzzy set theory. In the paper, vague data is defined as specialized fuzzy sets fuzzy numbers and a fuzzy linear regression model is described as a fuzzy function with fuzzy numbers as vague regression parameters. To identify the fuzzy coefficients of the model, the genetic algorithm is used....

The octagonal mesh is a variation of the two-dimensional (2D) mesh topology in which each processing element is connected to its eight closest neighbors. This paper studies the octagonal mesh as a topology for a wormhole-routed multiprocessor. A unicast routing algorithm and two multicast routing algorithms are presented and shown to be deadlock-free. Simulation results are given that compare m...

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found. PACS numbers: 05.20.-y, 05.50.+q, 04.20.Jb, 61.44.Br Short title: Solution of a decagonal random tiling February 1, 2008 † Elect...

Uncertainty plays a significant role in modeling and optimization of real world systems. Among uncertain approaches, fuzziness describes impreciseness while for ambiguity another definition is required. Vagueness is a probabilistic model of uncertainty being helpful to include ambiguity into modeling different processes especially in industrial systems. In this paper, a vague set based on dista...

In this study, an octagonal-based self-organizing network’s lattice structure is proposed to allow more exploration and exploitation in updating the weights for better mapping and classification performances. The neighborhood of the octagonal-based lattice structure provides more nodes for the weights updating than standard hexagonal-based lattice structure. Based on our experiment, the octagon...

we present a new renormalization-group calculation of the octagonal tiling excitation spectrum. Two new self-;imilar octagonal tilings are introduced, a triangle-Lite and a triangle-dan tiling, which are entangled with the standard rhombus-~quare tiling. The decimation procedure involved in the renormalization group calculation transforms each tiling enta a different one and goe; back tu the (r...

Take the vague predicate ‘tall’: I claim that any numbers assigned in an attempt to capture the vagueness of ‘tall’ do no more than serve as another measure of height. More generally, in so far as it is possible to assign numbers which respect certain truths about, for example, comparative relations, this is no more than a measure of an attribute related to, or underlying, the vague predicate. ...