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.
In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
In view of the main weaknesses of current fuzzy neural networks such as low reasoning precision and long training time, an Additive Multiplicative Fuzzy Neural Network (AMFNN) model and its architecture are present...In view of the main weaknesses of current fuzzy neural networks such as low reasoning precision and long training time, an Additive Multiplicative Fuzzy Neural Network (AMFNN) model and its architecture are presented. AMFNN combines additive inference and multiplicative inference into an integral whole, reasonably makes use of their advantages of inference and effectively overcomes their weaknesses when they are used for inference separately. Here, an error back propagation algorithm for AMFNN is presented based on the gradient descent method. Comparisons between the AMFNN and six representative fuzzy inference methods shows that the AMFNN is characterized by higher reasoning precision, wider application scope, stronger generalization capability and easier implementation.展开更多
This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given incon...This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.展开更多
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.
文摘In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
文摘In view of the main weaknesses of current fuzzy neural networks such as low reasoning precision and long training time, an Additive Multiplicative Fuzzy Neural Network (AMFNN) model and its architecture are presented. AMFNN combines additive inference and multiplicative inference into an integral whole, reasonably makes use of their advantages of inference and effectively overcomes their weaknesses when they are used for inference separately. Here, an error back propagation algorithm for AMFNN is presented based on the gradient descent method. Comparisons between the AMFNN and six representative fuzzy inference methods shows that the AMFNN is characterized by higher reasoning precision, wider application scope, stronger generalization capability and easier implementation.
基金partially supported by National Natural Sciences Foundation of China (71271188,71272129,71301061,71471059)Ministry of Education Humanities and Social Sciences Youth Fund(13YJC630120)+2 种基金National Social Science Fund Project(12AZD111)Natural Sciences and Engineering Research Council of Canada(NSERC) under its Discovery Grant programthe Jiangsu ITO Strategy Research Base Grant
文摘This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.
