Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of complex uncertain sequences: convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely. In addition, relationships among them are discussed.

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Abstract. Although genetic algorithm (GA) has the ability to do quick and stochastic global search, it can't efficiently use the output information for systems. Ant algorithm (AA), on the other hand, is a parallelproceed and distributive-forward system with a relatively slow speed for carrying out its solution. Incorporating GA and AA can improve their merits one for another. In this paper, the model and the method from the combination of GA and AA are proposed. The convergence of the method based on the Markov theory is analyzed. The experiment and analysis are conducted on the NP-hard problems for the cases of TSP30 (Travel Salesman Problem 30 cities) and CHN144 (China 144 cities). This work proves that the satisfactory solution sequence is monotonically decreasing and convergent. The results of simulations show that not only this combined algorithm is a step-by-step convergent process, but also its speed and effect of solving are quite satisfactory.

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Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain delay differential equations being stable in measure, in mean and in moment will be derived. Finally, this paper will discuss the relationship among stability in measure, stability in mean and stability in moment.

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