A three-way decision method in a hybrid decision information system and its application in medical diagnosis

In the traditional two-way decision, there are only two kinds of decisions (i.e., acceptance and rejection). It will sometimes pay unnecessary costs when one makes decisions in this way. Therefore, a three-way decision is proposed to avoid losses that caused by error acceptance or false rejection in decision-making process. An information system is a database that represents relationships between objects and attributes. A hybrid information system is an information system where there exist many kinds of data (e.g., boolean, categorical, real-valued and set-valued data) and missing data. This paper proposes a three-way decision method in a hybrid decision information system. First, the hybrid distance between two objects based on the conditional attribute set in a given hybrid decision information system is developed. Then, the tolerance relation on the object set of this hybrid decision information system is obtained by using the hybrid distance. Next, as a natural extension of decision-theoretic rough set model in an information system, decision-theoretic rough set model in this hybrid decision information system is presented. Moreover, a three-way decision method based on this decision-theoretic rough set model is proposed by means of probability measure. Finally, an example of medical diagnosis is employed to illustrate the feasibility of the proposed method, which may provide an effective method for hybrid data analysis in real applications.