The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Derong Liu - One of the best experts on this subject based on the ideXlab platform.

  • two new operators in rough set theory with applications to fuzzy sets
    Information Sciences, 2004
    Co-Authors: Huaguang Zhang, Hongli Liang, Derong Liu
    Abstract:

    In this paper, two new operators are introduced for the rough set theory. Using them, two inequalities well known in the rough set theory can now be modified to become equalities. With this change, no information will be lost in the new expressions. Hence, many properties in rough set theory can be improved and in particular, the union, the intersection, and the complement operations can be redefined based on the two equalities. Furthermore, the collection of rough sets of an Approximation Space forms a Boolean algebra under these new operators. Finally, roughness properties of fuzzy sets are analyzed using the new operations.

Bingzhen Sun - One of the best experts on this subject based on the ideXlab platform.

  • fuzzy rough set on probabilistic Approximation Space over two universes and its application to emergency decision making
    Expert Systems, 2015
    Co-Authors: Bingzhen Sun, Xiangtang Chen
    Abstract:

    Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough Approximation of a fuzzy concept on a probabilistic Approximation Space over two universes. We first present the definition of a lower and upper Approximation of a fuzzy set with respect to a probabilistic Approximation Space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic Approximation Space over two universes. We then define the fuzzy probabilistic Approximation over two universes by introducing a probability measure to the Approximation Space over two universes. Then, we establish the fuzzy rough set model on the probabilistic Approximation Space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic Approximation Space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic Approximation over two universes to emergency decision-making in unconventional emergency management. We establish an approach to online emergency decision-making by using the fuzzy rough set model on the probabilistic Approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision-making in order to illustrate the validity of the proposed method.

  • decision theoretic rough fuzzy set model and application
    Information Sciences, 2014
    Co-Authors: Bingzhen Sun, Haiyan Zhao
    Abstract:

    This article investigates the rough Approximation of a fuzzy concept on a probabilistic Approximation Space. We propose the probabilistic rough fuzzy set by defining the conditional probability of a fuzzy event. Then we establish the model of probabilistic rough fuzzy set and discuss several properties in detail. Furthermore, three generalizations of probabilistic rough fuzzy set, namely, 0.5-probabilistic rough fuzzy set, variable precision probabilistic rough fuzzy set and Bayesian rough fuzzy set are reported. In order to give a systematic method of selecting parameters for the probabilistic rough fuzzy set, we propose a decision-theoretic rough fuzzy set. That is, we formulate a non-parametric definition of the probabilistic rough fuzzy set. Moreover, we illustrate the motivation and verify the validity of the decision-theoretic rough fuzzy set by using a credit card applicant decision-making problem. Furthermore, the interrelationship between the decision-theoretic rough fuzzy set and the probabilistic rough fuzzy set is explained. The main contribution of this paper is twofold. One is to extend the probabilistic rough set to fuzzy environment, i.e., the probabilistic rough fuzzy set model. Another is to present an approach to select parameters needed in probabilistic rough fuzzy set modeling by using the process of decision-making under conditions of risk.

  • rough set theory for the interval valued fuzzy information systems
    Information Sciences, 2008
    Co-Authors: Zengtai Gong, Bingzhen Sun, Degang Chen
    Abstract:

    The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341-356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2-3) (1990) 191-209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets. This paper deals with an interval-valued fuzzy information system by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory and discusses the basic rough set theory for the interval-valued fuzzy information systems. In this paper we firstly define the rough Approximation of an interval-valued fuzzy set on the universe U in the classical Pawlak Approximation Space and the generalized Approximation Space respectively, i.e., the Space on which the interval-valued rough fuzzy set model is built. Secondly several interesting properties of the Approximation operators are examined, and the interrelationships of the interval-valued rough fuzzy set models in the classical Pawlak Approximation Space and the generalized Approximation Space are investigated. Thirdly we discuss the attribute reduction of the interval-valued fuzzy information systems. Finally, the methods of the knowledge discovery for the interval-valued fuzzy information systems are presented with an example.

J Trevelyan - One of the best experts on this subject based on the ideXlab platform.

  • singular enrichment functions for helmholtz scattering at corner locations using the boundary element method
    International Journal for Numerical Methods in Engineering, 2020
    Co-Authors: B D Gilvey, J Trevelyan, G Hattori
    Abstract:

    In this paper we use an enriched Approximation Space for the efficient and accurate solution of the Helmholtz equation in order to solve problems of wave scattering by polygonal obstacles. This is implemented in both Boundary Element Method (BEM) and Partition of Unity Boundary Element Method (PUBEM) settings. The enrichment draws upon the asymptotic singular behaviour of scattered fields at sharp corners, leading to a choice of fractional order Bessel functions that complement the existing Lagrangian (BEM) or plane wave (PUBEM) Approximation Spaces. Numerical examples consider configurations of scattering objects, subject to the Neumann ‘sound hard’ boundary conditions, demonstrating that the approach is a suitable choice for both convex scatterers and also for multiple scattering objects that give rise to multiple reflections. Substantial improvements are observed, significantly reducing the number of degrees of freedom required to achieve a prescribed accuracy in the vicinity of a sharp corner.

  • novel basis functions for the partition of unity boundary element method for helmholtz problems
    International Journal for Numerical Methods in Engineering, 2013
    Co-Authors: M J Peake, J Trevelyan, Graham Coates
    Abstract:

    The BEM is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains. In the last decade, the partition of unity BEM, in which the Approximation Space is enriched with a linear combination of plane waves, has been developed; this significantly reduces the number of DOFs required per wavelength. It has been shown that the element ends are more susceptible to errors in the Approximation than the mid-element regions. In this paper, the authors propose that this is due to the use of a collocation approach in combination with a reduced order of continuity in the Lagrangian shape function component of the basis functions. It is demonstrated, using numerical examples, that choosing trigonometric shape functions, rather than classical polynomial shape functions (quadratic in this case), provides accuracy benefits. Collocation schemes are investigated; it is found that the somewhat arbitrary choice of collocating at equally Spaced points about the surface of a scatterer is better than schemes based on the roots of polynomials or consideration of the Fock domain.

  • a partition of unity fem for time dependent diffusion problems using multiple enrichment functions
    International Journal for Numerical Methods in Engineering, 2013
    Co-Authors: Shadi M Mohamed, J Trevelyan, Mohammed Seaid, Omar Laghrouche
    Abstract:

    An enriched partition of unity FEM is developed to solve time-dependent diffusion problems. In the present formulation, multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element Approximation Space. The resulting enrichment is in the form of a local asymptotic expansion. Unlike previous works in this area where the enrichment must be updated at each time step, here, the temporal decay in the solution is embedded in the asymptotic expansion. Thus, the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right-hand side of the linear system of equations. The advantage is a significant saving in the computational effort where, previously, the linear system must be reevaluated and resolved at every time step. In comparison with the traditional finite element analysis with p-version refinements, the present approach is much simpler, more efficient, and yields more accurate solutions for a prescribed number of DoFs. Numerical results are presented for a transient diffusion equation with known analytical solution. The performance of the method is analyzed on two applications: the transient heat equation with a single source and the transient heat equation with multiple sources. The aim of such a method compared with the classical FEM is to solve time-dependent diffusion applications efficiently and with an appropriate level of accuracy.

  • novel basis functions for the partition of unity boundary element method for helmholtz problems
    10th World Congress on Computational Mechanics, 2012
    Co-Authors: M J Peake, J Trevelyan, Graham Coates
    Abstract:

    The boundary element method (BEM) is a popular tool for wave scattering prob- lems. To reduce the number of degrees of freedom required, the partition of unity BEM (PU- BEM) was developed in which the Approximation Space is enriched with a linear combination of plane-waves. Recent work has shown that the element ends are more susceptible to errors in the Approximation than the mid-element regions. In this paper we propose that this is due to the reduced order of continuity in the Lagrangian shape function component of the basis func- tions. It will demonstrated that choosing trigonometric shapes functions, rather than classical quadratic shape functions, provides accuracy benefits.

Huaguang Zhang - One of the best experts on this subject based on the ideXlab platform.

  • two new operators in rough set theory with applications to fuzzy sets
    Information Sciences, 2004
    Co-Authors: Huaguang Zhang, Hongli Liang, Derong Liu
    Abstract:

    In this paper, two new operators are introduced for the rough set theory. Using them, two inequalities well known in the rough set theory can now be modified to become equalities. With this change, no information will be lost in the new expressions. Hence, many properties in rough set theory can be improved and in particular, the union, the intersection, and the complement operations can be redefined based on the two equalities. Furthermore, the collection of rough sets of an Approximation Space forms a Boolean algebra under these new operators. Finally, roughness properties of fuzzy sets are analyzed using the new operations.

Graham Coates - One of the best experts on this subject based on the ideXlab platform.

  • novel basis functions for the partition of unity boundary element method for helmholtz problems
    International Journal for Numerical Methods in Engineering, 2013
    Co-Authors: M J Peake, J Trevelyan, Graham Coates
    Abstract:

    The BEM is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains. In the last decade, the partition of unity BEM, in which the Approximation Space is enriched with a linear combination of plane waves, has been developed; this significantly reduces the number of DOFs required per wavelength. It has been shown that the element ends are more susceptible to errors in the Approximation than the mid-element regions. In this paper, the authors propose that this is due to the use of a collocation approach in combination with a reduced order of continuity in the Lagrangian shape function component of the basis functions. It is demonstrated, using numerical examples, that choosing trigonometric shape functions, rather than classical polynomial shape functions (quadratic in this case), provides accuracy benefits. Collocation schemes are investigated; it is found that the somewhat arbitrary choice of collocating at equally Spaced points about the surface of a scatterer is better than schemes based on the roots of polynomials or consideration of the Fock domain.

  • novel basis functions for the partition of unity boundary element method for helmholtz problems
    10th World Congress on Computational Mechanics, 2012
    Co-Authors: M J Peake, J Trevelyan, Graham Coates
    Abstract:

    The boundary element method (BEM) is a popular tool for wave scattering prob- lems. To reduce the number of degrees of freedom required, the partition of unity BEM (PU- BEM) was developed in which the Approximation Space is enriched with a linear combination of plane-waves. Recent work has shown that the element ends are more susceptible to errors in the Approximation than the mid-element regions. In this paper we propose that this is due to the reduced order of continuity in the Lagrangian shape function component of the basis func- tions. It will demonstrated that choosing trigonometric shapes functions, rather than classical quadratic shape functions, provides accuracy benefits.