Computational Unified Set Theory and Application

The computational unified set model （CUSM） as the latest progress of Unified Set theory is introduced in this paper. The model combines unified set theory, information granule, complex adaptive system and cognitive science to present a new approach to simulate the cognition of human beings that can be viewed as the evolutionary process through the automatic learning from data sets. The information granule, which is the unit of cognition in CUSM, can be synthesized and created by the basic operators. It also can form the granule network by linking with other granules. With the learning from database, the system can evolve under the pressure of selection. As the adaptive results, fuzzy sets, vague sets and rough sets, etc can emerge out spontaneously. The CUSM answers the question of the origin of the uncertainties in thinking process described by unified set theory, that is due to the emergent properties of a holistic system of multiple cognitive units. And also the CUSM creates a dynamic model that can adapt to the environment. As a result, the ＂closed world＂ limitation in machine learning may be broken. The paper also discusses the applications of CUSM in roles discovery, problem solving, clustering analysis and data mining etc. The main features of the model comparing with the classical approaches toward those problems are its adaptability, flexibility and robustness but not accuracy.