Approximate theorem of positive continuous additive functionals is discussed and then used to give a d-dimensional analogue to the representation of additive functiouals of one-dimensional Brownian Motion with respect...Approximate theorem of positive continuous additive functionals is discussed and then used to give a d-dimensional analogue to the representation of additive functiouals of one-dimensional Brownian Motion with respect to local time.展开更多
There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the...There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the fuzzy number space(E^n,D).In this paper,asuitable semi-order in the fuzzy number space(E^n,D)and the semi-order fuzzy supermartingale and submar-tingale are introduced,the charaterlstics of semi-ordersupermartingales and submartingales,as well as theDood’s stopping theorem for them(the bounded stoppingtimes theorem and the general stopping times theoremfor a class of closable semi-order fuzzy supermartin-gales and submartingales)are established.展开更多
Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-compos...Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.展开更多
There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper,common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metr...There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper,common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp or D*p, 1 ≤ p ＜∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comme nts on the convergence of LRfuzzy number sequences are represented.展开更多
Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and un...Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to展开更多
The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy rand...The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.展开更多
文摘Approximate theorem of positive continuous additive functionals is discussed and then used to give a d-dimensional analogue to the representation of additive functiouals of one-dimensional Brownian Motion with respect to local time.
文摘There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the fuzzy number space(E^n,D).In this paper,asuitable semi-order in the fuzzy number space(E^n,D)and the semi-order fuzzy supermartingale and submar-tingale are introduced,the charaterlstics of semi-ordersupermartingales and submartingales,as well as theDood’s stopping theorem for them(the bounded stoppingtimes theorem and the general stopping times theoremfor a class of closable semi-order fuzzy supermartin-gales and submartingales)are established.
文摘Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.
文摘There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper,common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp or D*p, 1 ≤ p ＜∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comme nts on the convergence of LRfuzzy number sequences are represented.
文摘Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to
文摘The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.
