We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior...We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.展开更多
This paper proposes a vague decision method for analog circuit fault diagnosis based on description sphere. Firstly, the proposed method uses the wavelet transform as the preprocessor to extract fault features from th...This paper proposes a vague decision method for analog circuit fault diagnosis based on description sphere. Firstly, the proposed method uses the wavelet transform as the preprocessor to extract fault features from the output voltages of the circuit un- der test （CUT）. And then, each class sample is trained to produce a minimum description sphere. Finally, the test samples are detected by a defined vague decision rule, which is based on the vague weight distance between the test data and the center of description sphere. The defined decision rule fuses the truth and false membership degrees of the test sample and the weight of the description sphere, and it can effectively deal with the uncertain information. The reliability of the defined decision rule is proved theoretically. This new diagnostic method is first applied to testing two actual circuits, and then it is compared with other two diagnostic methods. The experimental results show that the proposed technique can achieve good performance and reduce the diagnostic time.展开更多
Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian...Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .展开更多
In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung n...In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed.展开更多
To remedy the defects of the existing research achievements,the dynamic vague region relations without kernel and the non-same-plane vague region relations without kernel based on the conception of the vague sets were...To remedy the defects of the existing research achievements,the dynamic vague region relations without kernel and the non-same-plane vague region relations without kernel based on the conception of the vague sets were studied systematically.The formalized definitions of the vague intersection set,the vague cut sets and vague region partition etc were given.Based on the vague sets,the eight vague region relations in the same plane and the ten vague region relations in the different plane were given.Furthermore,the coessential intersection and the heterogeneous intersection were proposed to simplify the representation for the dynamic vague region relations without kernel and the rotation-corresponding relations between the two kinds of the relations were also studied.The production in this paper laid the foundation for the applications and research of the vague region relations without kernel in the spatial database.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No.10071003).
文摘We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.
基金National Natural Science Foundation of China （60871009） Aeronautical Science Foundation of China （2009ZD52045） Funding of Jiangsu Innovation Program for Graduate Education （CX10B_098Z）
文摘This paper proposes a vague decision method for analog circuit fault diagnosis based on description sphere. Firstly, the proposed method uses the wavelet transform as the preprocessor to extract fault features from the output voltages of the circuit un- der test （CUT）. And then, each class sample is trained to produce a minimum description sphere. Finally, the test samples are detected by a defined vague decision rule, which is based on the vague weight distance between the test data and the center of description sphere. The defined decision rule fuses the truth and false membership degrees of the test sample and the weight of the description sphere, and it can effectively deal with the uncertain information. The reliability of the defined decision rule is proved theoretically. This new diagnostic method is first applied to testing two actual circuits, and then it is compared with other two diagnostic methods. The experimental results show that the proposed technique can achieve good performance and reduce the diagnostic time.
文摘Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .
基金supported by the National Research Foundation of Korea(NRF)Grant funded by the Korea government(MSIT)(No.RS-2023-00218176)Korea Institute for Advancement of Technology(KIAT)Grant funded by the Korea government(MOTIE)(P0012724)The Competency Development Program for Industry Specialist)and the Soonchunhyang University Research Fund.
文摘In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed.
基金Sponsored by the Science and Tecnology Research Project of Education Department Heilongjiang Province(Grant No.11551084)
文摘To remedy the defects of the existing research achievements,the dynamic vague region relations without kernel and the non-same-plane vague region relations without kernel based on the conception of the vague sets were studied systematically.The formalized definitions of the vague intersection set,the vague cut sets and vague region partition etc were given.Based on the vague sets,the eight vague region relations in the same plane and the ten vague region relations in the different plane were given.Furthermore,the coessential intersection and the heterogeneous intersection were proposed to simplify the representation for the dynamic vague region relations without kernel and the rotation-corresponding relations between the two kinds of the relations were also studied.The production in this paper laid the foundation for the applications and research of the vague region relations without kernel in the spatial database.
