Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we study the relationships between mset relations and mset topology. Moreover, this paper concerns generalized mset approximation spaces via topological methods ...

A strategy is implemented to find the improved configuration design of an existing aircraft structure by executing topology and shape optimizations. Structural analysis of the Initial Design Space is performed in ANSYS under the loads pertinent to operating and ground conditions. By using the FEA results and data, an initial optimized layout configuration is attained by exploiting nonparametric...

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N . We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölderor modulus topology, appears as special case. © 2007 Elsevier Masson SAS. All rights reserved. Résumé Nous etudions les princ...

Rough set theory is a paradigm for approximate reasoning based on the assumption that concepts are divided into exact and non–exact (called also rough) ones by means of a topological structure induced by a representation of knowledge as a classification. A classification in its most simple form is an equivalence relation on a universe of objects; the classification induces a partition topology ...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

where 0 ≤ s ≤ t ≤ 1 and ⊗ denotes a tensor product. Lyons [17] proved that solutions of stochastic differential equations (SDEs) are continuous functions of the Brownian rough path w(s, t) = ( w(s, t)1, w(s, t)2). We give a precise definition of the Brownian rough path in the next section; see also [18] and [15]. The discontinuity of solutions of SDEs in the uniform convergence topology of w ca...

Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the higher-dimensional diagrams one draws to represent these structures can be taken quite literally as pieces of topology. Examples of this are the braids in a ...

For a bounded domain Ω ⊂ Rm,m ≥ 2, of class C0, the properties are studied of fields of ‘good directions’, that is the directions with respect to which ∂Ω can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good directions defined in a suitable neighbourhood of ∂Ω, in terms of which a corresponding flow can be defined. Using...

In systems characterized by a rough potential-energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and splitting of metastable states, have nontrivial effects on such networks and must be taken into account. We do this by means of a recently proposed renormalization...