A three-way decision method in a hybrid decision information system and its application in medical diagnosis
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A three‑way decision method in a hybrid decision information system and its application in medical diagnosis Zhaowen Li1 · Ningxin Xie2 · Dan Huang3 · Gangqiang Zhang2
© Springer Nature B.V. 2020
Abstract 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 threeway 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. Keywords Three-way decision · Method · Hybrid information system · Decision-theoretic rough set · Probability measure · Medical diagnosis · Feasibility * Ningxin Xie [email protected] * Dan Huang [email protected] Zhaowen Li [email protected] 1
Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin 537000, Guangxi, People’s Republic of China
2
School of Software and Information Security, Guangxi University for Nationalities, Nanning 530006, Guangxi, People’s Republic of China
3
School of Mathematics and Statistics Science, Baise University, Baise 533000, Guangxi, People’s Republic of China
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1 Introduction 1.1 Research background and related works Rough set theory, proposed by Pawlak (1982), is a valid tool for dealing with uncertainty information. Based on rough set theory, (Pawlak 2012) presented an information system as a database that represents relationships between objects and attributes. To date, rough set theory has been widely used in many fields, such as uncertainty modeling (Swiniarski and Skowron 2003), reasoning with uncertainty (Yao 1998), rule extraction (Kryszkiewicz 1999; Wang et al. 2007), classification and feature selection (Hu et al. 2010; Yang et al. 2007), these fields are associated with information sys
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