A three-way decision method in a fuzzy condition decision information system and its application in credit card evaluati
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ORIGINAL PAPER
A three-way decision method in a fuzzy condition decision information system and its application in credit card evaluation Zhaowen Li1 • Dan Huang2 Received: 15 January 2019 / Accepted: 27 April 2019 Ó Springer Nature Switzerland AG 2019
Abstract An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. A fuzzy condition decision information system(fc-decision information system) is a decision information system where each condition attribute is fuzzy. This paper proposes a three-way decision method in a fc-decision information system and gives its application in credit card evaluation. Gaussian kernel based on fuzzy Euclid distance between fuzzy sets is first acquired. Then the fuzzy Tcos-equivalence relation, induced by a given fcdecision information system, is obtained using Gaussian kernel. Next, based on approximately equal relation (ae-relation) between fuzzy sets, decision-theoretic rough set model in this fc-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 measures of sets. Finally, an example of credit card evaluation is employed to illustrate the feasibility of the proposed method. Keywords Three-way decision Fuzzy condition decision information system Method Decision-theoretic rough set Gaussian kernel ae-Relation Credit card evaluation
1 Introduction 1.1 Research background Rough set theory, presented by Pawlak (1982), is a new mathematical tool that can effectively handle various incomplete information, such as inaccuracy, inconsistency and incompleteness Pawlak and Skowron (2006). Rough set theory divides the universe into several equivalence classes using equivalence relations, and introduces upper and lower approximations to describe the uncertainty of knowledge. Through these equivalence relations, the
& Zhaowen Li [email protected] Dan Huang [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 Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, People’s Republic of China
universe is separated into three disjoint regions: positive region, negative region and boundary region. In practical application, this division is too strict and directly eliminates invalid attributes, resulting in high cost of division. Three-way decision, introduced by Yao (2007), meets the actual cognitive ability of human beings of a decisionmaking method in the process of studying probability and rough set theory (Yao 2009, 2010, 2011; Yao and Herbert 2007). This method gives positive region, negative region and boundary region to good semantic interpretations. More concretely, using these three regions, three-way decision method is pr
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