Cost-sensitive Multi-category Classification And Multi-objective Decision Based On Decision- Theoretic Rough Set

Rough set theory is introduced by Poland scholar Z.Pawlak in 1982, which is an effective mathematical tool for dealing with the imprecise and uncertain information. It regards knowledge as the indiscernible relation and introduces the concept of upper and lower approximation to depict the uncertain degree of knowledge. In the classical rough set, the upper and lower approximation sets is defined by the algebraic inclusion relation based on equivalence classes and concept classes. On this basis, the concept of positive region, negative region and boundary region have been defined. But those concepts were lack of semantic interpretation. Decision-theoretic model is a probabilistic extension of the classical rough set, which extends the algebraic inclusion relation to the adjustable inclusion relation of probability theory. Three-way decision is a further improvement on methodology of decision-theoretic rough set, which gives the semantic interpretation of positive region, negative region and boundary region according with human’s cognition. The theory says:In the actual decision process, people will immediately make a quick decision for the things they are sure of receiving or rejecting, but will delay the judgment for the things they couldn’t make a decision right now, that means take a deferred decision. So, By taking the boundary region as a deferred decision, three-way decision reduces the cost of false receiving or false rejecting, and accords to the human’s thinking pattern in decision processes, which has a great superiority. At present, three-way decision has been used in many fields, like medical system, investment management, teaching assessment and so on.But there exits two following problems of three-way decision:1) Most of those researches and application are based on two-category classification and it isn’t hold in real life. We need to consider multi-category classification problems. For example, in medical diagnosis, doctors not only need to know whether patients have a cold or not, but also want to know which disease the patients have, such as cold, pneumonia or other disease.2) Most of those researches only have one decision objective, namely single objective decision. While there are a lot of multi-category classification problems in practice. So the paper proposes two improvements about multi-category classification and multi-objective decision based on decision-theoretic rough set, and the main research contents are as follows:(1) Basing on decision-theoretic rough set, and adding a deferred region in three-way decision thought, this paper changes m-category classification problem (m>2) into (m+l)-category classification problem and proposes a new cost-sensitive multi-category classification model to deal with multi-category decision problems. According to Bayesian minimum risk decision theory, the new model not only considers the costs of misclassification of different categories are different, but also makes the finally decision results without decision conflict. The case analysis and experimental results demonstrate the effectiveness of the new model. Based on this new model, a distributed attribute reduction algorithm is given.(2) Basing on three-way decision, and using the conception of optimistic and pessimistic in multi-granularity rough set model, the paper defines the optimistic and pessimistic decision based on double-objective decision. Then the paper proposes the multi-objective decision and gives the decision rules in the model by using Bayesian minimum risk decision theory and weighting the cost-function in three-way decision model. Simultaneously, the paper discusses division of decision region under double-objective decision and gives the method of computing the decision regions. At last, the paper verifies the effectiveness of the model with an example.