Cost-sensitive Rough Set Theory: Model And Application

As one of the important approaches for intelligent information processing, rough set theory plays a fundamental role in the imitating of human brain’s thinking and cognition. With rapid development of technology, the structures and forms of data sets in real world applications become more and more complicated and diversification. The classical rough set theory is unable to deal with the real world applications. Hence, generalizing related concepts is the key to apply such theory dealing with complex applications. In this paper, three different viewpoints are considered, they are dynamic updating of data, test cost sensitivity, and decision cost sensitivity. By studying rough data set model and attribute reduction in terms such three viewpoint, the following research results are obtained:1. Non-monotonicity attribute reduction of decision-theoretic rough set. In decision-theoretic rough set model, the lower and upper approximations may increase or decrease with respect to the increasing of attributes. From the viewpoint of optimization, fitness functions of the decision-monotonicity criterion, generality criterion and cost criterion have been proposed respectively in this paper. Genetic algorithm is also applied to compute reducts. The experimental results show that: the reducts based on decision-monotonicity criterion can generate more positive region rules; the reducts based on generality criterion can generate most positive region rules; the reducts based on cost criterion can obtain lowest decision costs.2. Dynamic updating multigranulation fuzzy rough set. Dynamic updating of rough approximations and reducts are keys to the applications of the rough set theory in real data sets. In recent years, with respect to different requirements, many approaches have been proposed to study such problems. Nevertheless, few of the them are carried out under multigranulation fuzzy environment. The updating computations of multigranulation fuzzy rough approximations are explored in this paper. By considering the dynamic increasing of fuzzy granular structures, naive and fast algorithms are presented, respectively. Moreover, both naive and fast forward greedy algorithms are designed for granular structure selection in dynamic updating environment. Experiments on six datasets showing that fast algorithms are more effective for reducing computational time in comparison with naive algorithms.3. Modeling of test cost sensitive rough set. In incomplete information system, variable parameter classification relation is an improvement of the limited tolerance relation. However, it does not take the test costs of the attributes into consideration. To solve such a problem, a test-cost-sensitive based variable precision classification rough set is proposed. Furthermore, it should be noticed that the traditional heuristic algorithm does not take the importance of test cost of the attributes into account, while backtracking algorithm is very time consuming. Therefore, not only a new importance of the attribute is proposed, but also a new heuristic algorithm is presented for obtaining reduct with minor test cost. Finally, experimental results show the effectiveness of new algorithm by comparing with other algorithms.4. Generalization of decision-theoretic rough set model. Yao’s decision-theoretic rough set is based on the classical indiscernibility relation, such relation may be too strict in many applications. To solve this problem, a δ-cut decision-theoretic rough set is proposed. Furthermore, with respect to criteria of decision-monotonicity and cost decrease, two different algorithms are designed to compute reducts, respectively. The experimental results show that, with respect to the reducts based on decision-monotonicity criterion, the reducts based on cost minimum criterion can obtain lowest decision costs and largest approximation qualities.