Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuz...Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.展开更多
This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
Passive torque servo system (PTSS) simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturban...Passive torque servo system (PTSS) simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturbance is called extra torque. The most important issue for PTSS controller design is how to eliminate the influence of extra torque. Using backstepping technique, adaptive fuzzy torque control (AFTC) algorithm is proposed for PTSS in this paper, which reflects the essential characteristics of PTSS and guarantees transient tracking performance as well as final tracking accuracy. Takagi-Sugeno (T-S) fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied using small gain theorem and the control system is proved to be semiglobally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an electric load simulator (ELS), and the comparative experimental results indicate that AFTC controller is effective for PTSS.展开更多
A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel dist...A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel distributed compensation （PDC） and linear matrix inequality （LMI） approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling.Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability.Finally,the error caused by fuzzy modeling is considered and the input-to-state stable （ISS） method is used to design the adaptive compensation term to reduce the effect of the modeling error.By the small-gain theorem,the resulting closed-loop system is proved to be input-to-state stable.Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded.The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.展开更多
This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the d...Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG^*.展开更多
In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.
In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some ...In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.展开更多
In this paper,we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.
基金Supported by the Aeronautical Science Foundation(20115868009)the Open Project Program of Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education in Xiangtan University(2011ICIP04)+1 种基金the Program of 211 Innovation Engineering on Information in Xiamen University(2009-2011)the College Students Innovation Training Plan of Xianmen University~~
文摘Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.
文摘This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
基金National High-tech Research and Development Program of China (2009AA04Z412)"111" ProjectBUAA Fund of Graduate Education and Development
文摘Passive torque servo system (PTSS) simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturbance is called extra torque. The most important issue for PTSS controller design is how to eliminate the influence of extra torque. Using backstepping technique, adaptive fuzzy torque control (AFTC) algorithm is proposed for PTSS in this paper, which reflects the essential characteristics of PTSS and guarantees transient tracking performance as well as final tracking accuracy. Takagi-Sugeno (T-S) fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied using small gain theorem and the control system is proved to be semiglobally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an electric load simulator (ELS), and the comparative experimental results indicate that AFTC controller is effective for PTSS.
基金supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.07KJB510125,08KJD510008)the Natural Science Foundation of Yancheng Teachers University(No.07YCKL062,08YCKL053)
文摘A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel distributed compensation （PDC） and linear matrix inequality （LMI） approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling.Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability.Finally,the error caused by fuzzy modeling is considered and the input-to-state stable （ISS） method is used to design the adaptive compensation term to reduce the effect of the modeling error.By the small-gain theorem,the resulting closed-loop system is proved to be input-to-state stable.Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded.The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.
基金Supported by the National Natural Science Foundation of China (No. 69803007)
文摘This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
文摘Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG^*.
文摘In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.
基金Supported in part by the National Social Science Foundation of China(19BTJ020)。
文摘In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.
文摘In this paper,we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.
