Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

A new method of moving asymptotes for large-scale linearly equality-constrained minimization

A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed.In this method,linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved.The numerical results show that the new method may be capable of processing some large scale problems.     

PARAMETER IDENTIFICATION FOR THE DOUBLE POROSITY SYSTEMS IN FRACTURE RESERVOIRS

The inverse parameter problem of the permeable law of the naturally fractured reservoirs with double perosity is of great importance in the exploitation of oil The coefficients in the fluid motion equations are unknown geological parameters. In this paper, the history of matching problem of reservoir systems with double porosity has been discussed from the point of view of the parameter identification of distributed parameter systems, and the problems of identifiability and observability for this system are also dealt with. We have obtained the formulas of Fréchet derivative of the index functional in the identification parameters. These formulas are necessary for calculating identification parameters by a gradient or conjugate gradient method. The conditions of identifiability and observability for the reservoir system with double porosity are given.     

双极值模糊集在半环上的应用

On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

On uniqueness of （fuzzy） relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.     

European option pricing model in a stochastic and fuzzy environment

The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.     

FUZZY IDENTIFIER WITH EXPONENTIAL RATE OF CONVERGENCE FOR NONLINEAR DYNAMIC SYSTEMS

1 IntroductionIn recent yearst there is a development in the use of fuzzy systems for modelling, identifyingand controlling nonlinear systems. The reason is that conventional identification methods canonly use input-output pairs, but ignore linguistic information about the behavior of nonlinearsystems. Therefore, developing identifiers and controllers Of nonlinear systems which can com-bine both linguistic knowledge and numerical information is an important task. Ill this repect,works on the …     

A FLEXIBLE PRECONDITIONED ARNOLDI METHOD FOR SHIFTED LINEAR SYSTEMS

We are interested in the numerical solution of the large nonsymmetric shifted linear system, （A ＋ αI）x -= b, for many different values of the shift a in a wide range. We apply the Saad＇s flexible preconditioning technique to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.     

Jackknife empirical likelihood test for the equality of degrees of freedom in t-copulas

It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple parameters of degrees of freedom has been proposed in the literature, which generalizes both the t-copulas and the grouped t-copulas. Like the inference for a t-copula, a computationally efficient inference procedure is to first estimate the correlation matrix via Kendall's τ and then to estimate the parameters of degrees of freedom via pseudo maximum likelihood estimation. This paper proposes a jackknife empirical likelihood test for testing the equality of some parameters of degrees of freedom based on this two-step inference procedure, and shows that the Wilks theorem holds.     

On Existence of Ground States for Some Elliptic Systems

In this paper we consider the existence of ground states for some 2- coupled nonlinear Schrodinger systems with or without potentials. Under various conditions on the parameters in the equations, we prove the existence of ground states.     

MTL-代数的区间值$(\in,\in \vee q)$-模糊滤子

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.     

THE ＇HYBRID＇ TECHNIQUE FOR RISK ANALYSIS OF SOME DISEASES

Based on the data obtained from a survey recently made in Shanghai, this paper presents the hybrid technique for risk analysis and evaluation of some diseases. After determination of main risk factors of these diseases by analysis of variance, the authors introduce a new concept ‘Illness Fuzzy Set‘ and use fuzzy comprehensive evaluation to evaluate the risk of suffering from a disease for residents. Optimal technique is used to determinethe weights wi in fuzzy comprehensive evaluation, and a new method ‘Improved Information Distribution‘ is also introduced for the treatment of small sample problem. It is shown that the results obtained by using the hybrid technique are better than by using single fuzzy technique or single statistical method.     

The Same Distribution of Limit Cycles in a Hamiltonian System with Nine Seven-order Perturbed Terms

Using qualitative analysis and numerical simulation, we investigate the number and distribution of limit cycles for a cubic Hamiltonian system with nine different seven-order perturbed terms. It is showed that these perturbed systems have the same distribution of limit cycles. Furthermore, these systems have 13, 11 and 9 limit cycles for some parameters, respectively. The accurate positions of the 13, 11 and 9 limit cycles are obtained by numerical exploration, respectively. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.     

TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic travelingwaves for a class of nonlinear dispersive partial differential equations.By using the bifurcationtheory of dynamical systems to do qualitative analysis,all possible phase portraits in theparametric space for the traveling wave systems are obtained.It can be shown that the existenceof a singular straight line in the traveling wave system is the reason why smooth solitary wavesolutions converge to solitary cusp wave solution when parameters are varied.The differentparameter conditions for the existence of solitary and periodic wave solutions of different kindsare rigorously determined.     

模糊粗糙群中的同态映射(英文)

This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.     

Fuzzy幂群与Fuzzy商群的相互关系

In this paper,we extend the concept of fuzzy quotient groups.The structures of fuzzy power groups and fuzzy quotient groups are discussed.The relationship between fuzzy power groups and fuzzy quotient groups are considered.     

Exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.     

Fuzzy Rough Ring and Its Properties

This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.     

GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered.In fact,this is a generalization of quasi-coincidence of a fuzzy point With a fuzzy set.By using this new idea,the notion of interval valued(∈,∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras,is defined,and related properties are investigated.In particular,the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.