Partial ordering of information granulations: a further investigation

Authors

  • Yuhua Qian,

    1. Key Laboratory of Computational Intelligence, Chinese Information Processing of Ministry of Education, Taiyuan, China
    2. School of Computer, Information Technology, Shanxi University, Taiyuan, China
    3. Department of Manufacturing Engineering, Engineering Management, City University of Hong Kong, Hong Kong
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  • Chuangyin Dang,

    1. Department of Manufacturing Engineering, Engineering Management, City University of Hong Kong, Hong Kong
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  • Jiye Liang,

    1. Key Laboratory of Computational Intelligence, Chinese Information Processing of Ministry of Education, Taiyuan, China
    2. School of Computer, Information Technology, Shanxi University, Taiyuan, China
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  • Weizhi Wu

    1. School of Mathematics, Physic, Information Science, Zhejiang Ocean University, Zhoushan, China
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Abstract

The notion of information systems provides a convenient tool for knowledge representation of objects in terms of their attribute values, while partial ordering is usually used to research the rough monotonicity of an uncertainty measure in information systems. In this paper, we first reveal the limitations of existing partial orderings to describe information granulations in information systems with several illustrative examples. Then, a generalized partial ordering with a set-size nature is proposed to overcome their shortcoming and some of its important properties are derived. Finally, we prove that several existing information granulations all satisfy the granulation monotonicity induced by the proposed partial ordering. The presented partial ordering appears to be well suited to characterize the nature of information granulations in an information system. These results will be very helpful for studying granular computing and uncertainty in information systems.

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