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Entropy measurement for a hybrid information system with images: an application in attribute reduction

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Abstract

In the real world, there may exist manifold data (e.g., Boolean, categorical, real-valued, set-valued, interval-valued, image, decision and missing data or attributes) in an information system which is referred to as a hybrid information system with images (HISI). Handling an HISI is conducive to generalize applications of rough set theory. This paper studies entropy measurement for a hybrid information system with images and considers an application for attribute reduction. We first give the distance between information values on each attribute in an HISI. Then, we present tolerance relations on the object set of an HISI based on this distance. Next, we define the rough approximations in an HISI by means of the presented tolerance relations. Furthermore, we study entropy measurement for an HISI by using \(\theta \)-information entropy, \(\theta \)-conditional information entropy and \(\theta \)-joint information entropy. Based on Kryszkiewicz’s ideal, we introduce the concepts of \(\theta \)-generalized decision and \(\theta \)-consistent in an HISI. Finally, we apply entropy measurement to perform attribute reduction in a \(\theta \)-consistent HISI. It is worth mentioning that attribute reduction based on generalized decision and common attribute reduction in a \(\theta \)-consistent HISI are the same.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of this paper.

Funding

Funding was provided by National Natural Science Foundation of Guangxi (2022GXNSFAA035552, 2021GXNSFAA220114).

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Authors and Affiliations

  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

    Zhaowen Li

  2. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Yiying Chen

  3. School of Artificial Intelligence, Guangxi Minzu University, Nanning, 530006, Guangxi, People’s Republic of China

    Gangqiang Zhang, Liangdong Qu & Ningxin Xie

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  1. Zhaowen Li
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  2. Yiying Chen
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  3. Gangqiang Zhang
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  4. Liangdong Qu
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  5. Ningxin Xie
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Correspondence to Gangqiang Zhang.

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Li, Z., Chen, Y., Zhang, G. et al. Entropy measurement for a hybrid information system with images: an application in attribute reduction. Soft Comput 26, 11243–11263 (2022). https://doi.org/10.1007/s00500-022-07502-0

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