This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characterist...This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.展开更多
The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The useful...The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The usefulness of the proposed similarity measure was verified.The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions,though it was not easy to design.Through conventional results on the calculation of similarity for fuzzy membership pair,fuzzy membership-crisp pair and crisp-crisp pair were carried out.The proposed distance based similarity measure represented rational performance with the heuristic point of view.Furthermore,troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed.Finally,the similarity measure computation for various membership function pairs was discussed with other conventional results.展开更多
Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure ...Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure of fuzzy entropy was proposed by considering fuzzy membership through distance measure,and the obtained results contained more flexibility than the general fuzzy membership function.Furthermore,characteristic analyses for non convex function were also illustrated.Analyses on the mutual information were carried out through the proposed fuzzy entropy and similarity measure,which was also dual structure of fuzzy entropy.By the illustrative example,mutual information was discussed.展开更多
This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapu...This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.展开更多
Discuss the no-arbitrage principle in a fuzzy market and present a model for pricing an option. Get a fuzzy price for the contingent claim in a market involving fuzzy elements, whose level set can be seen as the possi...Discuss the no-arbitrage principle in a fuzzy market and present a model for pricing an option. Get a fuzzy price for the contingent claim in a market involving fuzzy elements, whose level set can be seen as the possible price level interval with given belief degree. Use fuzzy densit） function and fuzzy mean as evidence for such model. Also give an example for comparing the result of the model in this article and that of another pricing method.展开更多
Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy mo...Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).展开更多
In this paper, an example is given. It shows that there exists a fuzzy-valued function which is (K) integrable on [a, 6], but its primitive is not differentiable almost everywhere in [a, b].
This paper proposes a support vector machine-based fuzzy rules acquisition system(SVM-FRAS) .The character of SVM in extracting support vector provides a mechanism to extract fuzzy If-Then rules from the training data...This paper proposes a support vector machine-based fuzzy rules acquisition system(SVM-FRAS) .The character of SVM in extracting support vector provides a mechanism to extract fuzzy If-Then rules from the training data set.We construct the fuzzy inference system using fuzzy basis function(FBF) .The gradient technique is used to tune the fuzzy rules and the inference system.Theoretical analysis and comparative tests are performed comparing with other fuzzy systems.Experimental results show the SVM-FRAS model possesses good generalization capability as well as high comprehensibility.展开更多
文摘This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.
基金Project(2010-0020163) supported by Priority Research Centers Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education,Science and Technology
文摘The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The usefulness of the proposed similarity measure was verified.The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions,though it was not easy to design.Through conventional results on the calculation of similarity for fuzzy membership pair,fuzzy membership-crisp pair and crisp-crisp pair were carried out.The proposed distance based similarity measure represented rational performance with the heuristic point of view.Furthermore,troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed.Finally,the similarity measure computation for various membership function pairs was discussed with other conventional results.
基金Work supported by the Second Stage of Brain Korea 21 Projects Work(2010-0020163) supported by the Priority Research Centers Program through the National Research Foundation (NRF) funded by the Ministry of Education,Science and Technology of Korea
文摘Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure of fuzzy entropy was proposed by considering fuzzy membership through distance measure,and the obtained results contained more flexibility than the general fuzzy membership function.Furthermore,characteristic analyses for non convex function were also illustrated.Analyses on the mutual information were carried out through the proposed fuzzy entropy and similarity measure,which was also dual structure of fuzzy entropy.By the illustrative example,mutual information was discussed.
基金The National Natural Science Foundation of China(No.60764001,60835001,60875035,61004032)the Postdoctoral Research Fund of Southeast Universitythe Natural Science Foundation of Jiangsu Province(No.BK2008294)
文摘This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.
文摘Discuss the no-arbitrage principle in a fuzzy market and present a model for pricing an option. Get a fuzzy price for the contingent claim in a market involving fuzzy elements, whose level set can be seen as the possible price level interval with given belief degree. Use fuzzy densit） function and fuzzy mean as evidence for such model. Also give an example for comparing the result of the model in this article and that of another pricing method.
文摘Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).
基金Supported by National Natural Science Found of China(40235053),Natural Science Foundation of Gausu Province(ZS011-A25-012-Z)and NWNU-KJCXGC-212.
文摘In this paper, an example is given. It shows that there exists a fuzzy-valued function which is (K) integrable on [a, 6], but its primitive is not differentiable almost everywhere in [a, b].
基金the Shanghai Sciences and Technology Committee under Grant No.08DZ1202500 (No.08DZ1202502)the Young Faculty Research Grant of Shanghai Maritime Universitythe Shanghai Young Faculty Research Grant (No.shs08032)
文摘This paper proposes a support vector machine-based fuzzy rules acquisition system(SVM-FRAS) .The character of SVM in extracting support vector provides a mechanism to extract fuzzy If-Then rules from the training data set.We construct the fuzzy inference system using fuzzy basis function(FBF) .The gradient technique is used to tune the fuzzy rules and the inference system.Theoretical analysis and comparative tests are performed comparing with other fuzzy systems.Experimental results show the SVM-FRAS model possesses good generalization capability as well as high comprehensibility.
