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As an effective vehicle, uncertainty theory is applicable for handling subjective indeterminacy. Based on uncertainty theory, the Hurwicz model of the zero-sum uncertain differential game with jump is formulated, in which the dynamic system is portrayed by an uncertain differential equation satisfying both the canonical Liu process and V-jump uncertain process. An equilibrium equation for solving the saddle-point of the above game is proposed. In addition, the game with a linear dynamic system and the quadratic objective function is further analysed. At last, a resource extraction problem using our theoretical results is described. [ABSTRACT FROM AUTHOR]

In this correspondence, the impulsive effects on the stability of fuzzy Cohen-Grossberg neural networks (FCGNNs) with time-varying delays are considered. Several sufficient conditions are obtained ensuring global exponential stability of equilibrium point for the neural networks by the idea of vector Lyapunov function, M-matrix theory, and analytic methods. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results not only show that the stability still remains under certain impulsive perturbations for the continuous stable FCGNNs with time-varying delays, but also present an approach to stabilize the unstable FCGNNs with time-varying delays by utilizing impulsive effects. An example with simulations is given to show the effectiveness of the obtained results. Index Terms--Fuzzy Cohen--Grossberg neural networks (FCGNNs), global exponential stability, impulsive, time-varying delays.

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. Based on the concept of uncertain theory, this paper considers optimal control and zero-sum differential game for multi-factor uncertain continuous-time singular systems with Hurwicz criterion, where dynamic systems are modelled by a type of uncertain differential equation driven by canonical Liu process. Using the approach of dynamic programming, the principle of optimality is proposed and then the equation of optimality is derived to resolve an uncertain control model. A two-player zero-sum uncertain differential game is further investigated based on the optimality equation above, and an equilibrium equation is presented to locate a saddle-point in the game. Finally, an example is discussed to illuminate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

In reliability analysis of the J-out-of-N system, people usually assume that the lifetime of components in the system follows the exponential, Weibull or gamma distribution. However, this assumption has some limitations in fitting real-life data. Nadarajah–Haghighi distribution has more advantages than exponential, Weibull and gamma distributions in reliability modelling of real data. This paper investigates the reliability analysis of a J-out-of-N system in which the lifetimes of components follow Nadarajah–Haghighi distribution. Based on the generalised progressive hybrid censoring (GPHC) sample, the maximum likelihood estimates (MLEs), and the asymptotic confidence intervals of unknown parameters and the reliability function of the system are obtained by using the numerical procedure and asymptotic normality theory of MLEs, respectively. The Bayesian estimates under squared error loss are derived using the Tierney–Kadane's (T–K) method. Furthermore, the Bayesian credible intervals are constructed based on Metropolis–Hastings method. Monte Carlo simulations are carried out to evaluate the performance of the proposed estimation methods. Finally, two real data sets are analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]