Uncertainty measurement for interval-valued decision systems based on extended conditional entropy

  • Authors:

  • Jianhua Dai;Wentao Wang;Qing Xu;Haowei Tian

  • Affiliations:

  • College of Computer Science, Zhejiang University, Hangzhou 310027, China and Center for the Study of Language and Cognition, Zhejiang University, Hangzhou 310028, China;College of Computer Science, Zhejiang University, Hangzhou 310027, China;College of Computer Science, Zhejiang University, Hangzhou 310027, China;College of Computer Science, Zhejiang University, Hangzhou 310027, China

  • Venue:
  • Knowledge-Based Systems
  • Year:
  • 2012

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Abstract

Uncertainty measures can supply new points of view for analyzing data and help us to disclose the substantive characteristics of data sets. Some uncertainty measures for single-valued information systems or single-valued decision systems have been developed. However, there are few studies on the uncertainty measurement for interval-valued information systems or interval-valued decision systems. This paper addresses the uncertainty measurement problem in interval-valued decision systems. An extended conditional entropy is proposed in interval-valued decision systems based on possible degree between interval values. Consequently, a concept called rough decision entropy is introduced to evaluate the uncertainty of an interval-valued decision system. Besides, the original approximation accuracy measure proposed by Pawlak is extended to deal with interval-valued decision systems and the concept of interval approximation roughness is presented. Experimental results demonstrate that the rough decision entropy measure and the interval approximation roughness measure are effective and valid for evaluating the uncertainty measurement of interval-valued decision systems. Experimental results also indicate that the rough decision entropy measure outperforms the interval approximation roughness measure.