Soft Rough Approximation Operators on a Complete Atomic Boolean Lattice

The concept of soft sets based on complete atomic Boolean lattice, which can be seen as a generalization of soft sets, is introduced. Some operations on these soft sets are discussed, and new types of soft sets such as full, keeping infimum, and keeping supremum are defined and supported by some illustrative examples. Two pairs of new soft rough approximation operators are proposed and the relationship among soft set is investigated, and their related properties are given. We show that Järvinen's approximations can be viewed as a special case of our approximation. If , then our soft approximations coincide with crisp soft rough approximations (Feng et al. 2011)

Global well-posedness of the 3D Navier--Stokes equations perturbed by a deterministic vector field

We are concerned with the problem of global well-posedness of the 3D Navier--Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a regularization by a deterministic vector field. More precisely, we consider the vorticity form of the system perturbed by an additional transport type term. Such a perturbation conserves the enstrophy and therefore a priori it does not imply any smoothing. Our main result is a construction of a deterministic vector field $v=v(t,x)$ which provides the desired regularization of the system and yields global well-posedness for large initial data outside arbitrary small sets. The proof relies on probabilistic arguments developed by Flandoli and Luo, tools from rough path theory by Hofmanov\'a, Leahy and Nilssen and a new Wong--Zakai approximation result, which itself combines probabilistic and rough path techniques.Comment: 23 pages. We modified the statement of Theorem

A New Approach of Rough Set Theory for ‎Feature Selection and Bayes Net Classifier ‎Applied on Heart Disease Dataset

درسنا في هذا البحث اختيار الصفات بالاعتماد على نهج جديد من  خوارزمية مجموعة التقريب حيث تعتمد هذه الطريقة على اختيار الصفات الأكثر تاثيرا. لجئنا الى انتقاء الصفات اختصارا للوقت , وجود الصفة تؤثر على دقة النتائج او قد تكون الصفة غير متوفرة . تم تطبيق الخوارزمية على بيانات امراض القلب لاختيار افضل الصفات المؤثرة. ان المشكلة الرئيسية هو كيفية تشخيص الإصابة فيما لو كان مصاب بمرض القلب من عدمه.هذه المشكلة تمثل تحدي لان لا نسطيع اتخاذ القرار بصورة مباشرة. تعتمد الطريقة المقترحة على ترميز البيانات الاصلية .ان الناتج من هذه الخوارزميه هي الصفات الأكثر أهمية حيث تهمل الصفات السيئة والغير ضرورية.وتم تطبيق النتائج على خوارزمية شكبة بيزينت كخوارزمية للتنبؤ بالمرض وقد حصلنا على النتائج 82.17 , 83.49 , 74.58 عند استخدام جميع الصفات ,12 , 7 طول الصفات على التوالي.وتم تطبيق نتائج خوارزمية مجموعة التقريب الاصلية على خوارزمية البيزين وحصلنا على النتائج 58.41 ,81.51  عند استخدام 2 , 12 طول الصفات على التواليIn this paper a new approach of rough set features selection has been proposed. Feature selection has been used for several reasons a) decrease time of prediction b) feature possibly is not found c) present of feature case bad prediction. Rough set has been used to select most significant features. The proposed rough set has been applied on heart diseases data sets. The main problem is how to predict patient has heart disease or not depend on given features. The problem is challenge, because it cannot determine decision directly .Rough set has been modified to get attributes for prediction by ignored unnecessary and bad features. Bayes net has been used for classified method. 10-fold cross validation is used for evaluation. The Correct Classified Instances were 82.17, 83.49, and 74.58 when use full, 12, 7 length of attributes respectively. Traditional rough set has been applied, the minimum Correct Classified Instances were 58.41 and 81.51 when use 2 length of attributes respectivel

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Quantum and Boltzmann transport in the quasi-one-dimensional wire with rough edges

We study quantum transport in Q1D wires made of a 2D conductor of width W and length L>>W. Our aim is to compare an impurity-free wire with rough edges with a smooth wire with impurity disorder. We calculate the electron transmission through the wires by the scattering-matrix method, and we find the Landauer conductance for a large ensemble of disordered wires. We study the impurity-free wire whose edges have a roughness correlation length comparable with the Fermi wave length. The mean resistance and inverse mean conductance 1/ are evaluated in dependence on L. For L -> 0 we observe the quasi-ballistic dependence 1/ = = 1/N_c + \rho_{qb} L/W, where 1/N_c is the fundamental contact resistance and \rho_{qb} is the quasi-ballistic resistivity. As L increases, we observe crossover to the diffusive dependence 1/ = = 1/N^{eff}_c + \rho_{dif} L/W, where \rho_{dif} is the resistivity and 1/N^{eff}_c is the effective contact resistance corresponding to the N^{eff}_c open channels. We find the universal results \rho_{qb}/\rho_{dif} = 0.6N_c and N^{eff}_c = 6 for N_c >> 1. As L exceeds the localization length \xi, the resistance shows onset of localization while the conductance shows the diffusive dependence 1/ = 1/N^{eff}_c + \rho_{dif} L/W up to L = 2\xi and the localization for L > 2\xi only. On the contrary, for the impurity disorder we find a standard diffusive behavior, namely 1/ = = 1/N_c + \rho_{dif} L/W for L < \xi. We also derive the wire conductivity from the semiclassical Boltzmann equation, and we compare the semiclassical electron mean-free path with the mean free path obtained from the quantum resistivity \rho_{dif}. They coincide for the impurity disorder, however, for the edge roughness they strongly differ, i.e., the diffusive transport is not semiclassical. It becomes semiclassical for the edge roughness with large correlation length