Fuzzy Number Decision Rough Set Based On Incomplete Information System

For the value of the loss function in the classical decision-making rough set, we give an exact real number usually. With the complexity of the research object, such as the complexity of the decision-making environment, the uncertainty and the ambiguity and limitation of the human thinking, and the limited knowledge of the decision maker, the loss function is more and more difficult to evaluate accurately, that make the decision maker use some vague form unconsciously, such as interval number, triangular fuzzy number act.There is missing data or the data is not complete in an information system, which is called incomplete information system. In reality, there are a large number of incomplete information systems. Based on the incomplete information system, this paper introduces the fuzzy form of interval number and triangular fuzzy number into the decision rough set, and extends the application scope of the decision rough set by drawing on the existing decision theory and rough set theory. The main contents include the following aspects:Firstly, aiming at the problem of the probability of missing values in incomplete infor-mation systems, the similarity and the concept of L-cut are proposed in incomplete infor-mation systems. Thus, a similarity relation is defined to describe incomplete information systems. Based on this similarity relation, we derive the upper and lower approximations of decision matrices in the incomplete information system and the corresponding three decision regions.Secondly, considering the " multi-value" feature of the loss function in the actual de-cision problem in the incomplete information system, from the Bayes theory, the interval number of the uniformly distributed interval is introduced into the decision-theoretic rough set, The paper discusses the construction process of interval-valued decision-theoretic rough set theory and analyzes the related mathematical properties and criteria of interval-valued decision-theoretic rough set theory, and then puts forward the interval-valued decision-theoretic rough set model based on incomplete information system. An example of medical diagnosis validates the validity of the proposed model.Thirdly, aiming at the preference value of the special attribute value in the interval value in the incomplete information system, the triangular fuzzy number obeying the tri-angular distribution is introduced into the decision-theoretic rough set, and the triangular fuzzy decision rough set is proposed. With the help of the integer value sorting method, the decision rules of triangular fuzzy number decision-theoretic rough set model are extracted,and then the three thresholds of the triangular fuzzy number decision-theoretic rough set are deduced. Considering the risk attitude of the decision maker, the optimistic decision model and the pessimistic decision model are put forward based on the decision-theoretic rough set theory. Finally, the example proves that the method can highlight the maximum value of the main value, thereby reducing the classification error.Based on the incomplete information system, this paper introduces the interval number and triangular fuzzy number into the decision rough set, and studies the fuzzy form of the interval function and the triangular fuzzy number respectively. On the one hand, the research scope of decision-making rough set is extended. On the other hand, it provides a new method for dealing with incomplete information systems.