In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that the proposed entropy measure for Atanassov's intuitionistic fuzzy set is consistent by comparing it with other existing entropies.
Connections between uniform exponential expansiveness and complete admissibility of the pair $(c_0({\mathbb N}, X),c_0({\mathbb N}, X))$ are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.
This paper is concerned with the exponential H∞ filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and H∞ control problem. Then, a mean-square exponentially stable and Markovian jump filter is designed such that the filtering error system is mean-square exponentially stable and the H∞ performance of estimation error can be ensured. Besides, the derivative of discrete time-varying delay h(t) satisfies h˙(t)≤η and simultaneously the decay rate β can be finite positive value without equation constraint. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.
We consider inequalities between sums of monomials that hold for all p-Newton sequences. This continues recent work in which inequalities between sums of two, two-term monomials were combinatorially characterized (via the indices involved). Our focus is on the case of sums of three, two-term monomials, but this is very much more complicated. We develop and use a theory of exponential polynomial inequalities to give a sufficient condition for general monomial sum inequalities, and use the sufficient condition in two ways. The sufficient condition is necessary in the case of sums of two monomials but is not known if it is for sums of more. A complete description of the desired inequalities is given for Newton sequences of less than 5 terms., Charles R. Johnson, Carlos Marijuán, Miriam Pisonero, Michael Yeh., and Obsahuje seznam literatury
Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in L1
are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is used as an illustration.
The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright's modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order for irregular data is derived. A similar method using a DLS () estimation of polynomial trend of order is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.
Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied mainly to various types of exponential smoothing (recursive estimation in Box-Jenkins models with outliers is also mentioned). The methods are demonstrated using simulated data.
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.
In this paper, the exponential stability of periodic solutions for inertial Cohen-Grossberg-type neural networks are investigated. First, by properly chosen variable substitution the system is transformed to first order differential equation. Second, some sufficient conditions which can ensure the existence and exponential stability of periodic solutions for the system are obtained by using constructing suitable Lyapunov function and differential mean value theorem, applying the analysis method and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.
In this paper, stochastic interval Hopfield neural networks with time-varying delays are investigated. By applying the Razumikhin-type theorem as well as inequality technique, a set of novel sufficient criteria independent of delays are given for the exponential stability of such networks. As a by-product, for the deterministic Hopfield neural networks with time-varying delays, some delay-independent criteria for their global exponential robust stability are also obtained. The proposed results improve and extend them in the earlier literature and are easier to verify. A numerical example and simulation are also given to illustrate the effectiveness of our results.