Supported by the National Natural Science Foundation of China under Grant Nos.60375016, 60496323 (国家自然科学基金)
Uncertainty exists widely in the subjective and objective world. In all kinds of uncertainty, randomness and fuzziness are the most important and fundamental. In this paper, the relationship between randomness and fuzziness is discussed. Uncertain states and their changes can be measured by entropy and hyper-entropy respectively. Taken advantage of entropy and hyper-entropy, the uncertainty of chaos, fractal and complex networks by their various evolution and differentiation are further studied. A simple and effective way is proposed to simulate the uncertainty by means of knowledge representation which provides a basis for the automation of both logic and image thinking with uncertainty. The AI (artificial intelligence) with uncertainty is a new cross-discipline, which covers computer science, physics, mathematics, brain science, psychology, cognitive science, biology and philosophy, and results in the automation of representation, process and thinking for uncertain information and knowledge.