Factor selection of product quotation with incomplete covering rough set

Abstract

Factor selection is crucial for any enterprise to make a quick and accurate quotation decision. For the objects of quotation with missing values, traditional rough sets construct their relations (e.g. tolerance, cover) either with objects having known values, or only with those that also include the missing values of the attribute domains. Such classifications may not work well for reduction in many real-world problems. In this paper, by measuring the similarity of objects, an incomplete covering rough set is proposed to derive a cover for attribute reduction. Firstly, a similarity relation is defined by an approximation degree that tunes the relation in line with the semantics of objects, and then a cover is induced. Secondly, a reduct is derived by the relations of objects with respect to covers; the properties of reduction are proven. Finally, an approach is developed by discernibility matrix. The experimental results of the UCI (University of California Irvine) Repository and real-life quotation data sets show the incomplete covering rough set outperforms the compared rough set in the accuracy of factor selection within the comparable computation time. It is also demonstrated that the proposed quotation model is effective in quote prediction with various proportions of missing data.

KEYWORDS:

• Factor selection
• quotation
• attribute reduction
• covering rough set
• incomplete information system

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant [No. 71874019], the National Social Science Foundation of China under Grant [No. 19BGL029], the Humanities and Social Science Fund of Ministry of Education of China under Grant [No. 20YJA630047], and National Defense Basic Scientific Research Program of China under Grant [No. JCKY2019205B012].

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

One of datasets used during the study is available in UCI Machine Learning Repository at https://archive.ics.uci.edu/ml/datasets/Breast+Tissue; the other dataset is included in Appendix.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 71874019]; Humanities and Social Science Fund of Ministry of Education of China [grant number 20YJA630047]; National Social Science Foundation of China [grant number 19BGL029]; National Defense Basic Scientific Research Program of China [grant number JCKY2019205B012].

Notes on contributors

Qiunan Meng

Qiunan Meng is an Associate Professor of School of Economics and Management, Dalian University of Technology. She has a PhD from Dalian University of Technology in China. Her main research interests include enterprise cost control, scheduling, machine learning and optimisation algorithms. She has published her work in international journals and conference papers. She has also led several research projects in China.

Xun Xu

Xun Xu is a Professor of Smart Manufacturing at the Department of Mechanical Engineering, The University of Auckland. He has a PhD from the University of Manchester. Dr. Xu is an internationally recognised expert in smart manufacturing systems, cloud-based manufacturing and IoT enabled manufacturing. Dr. Xu is the Director of Laboratory for Industry 4.0 Smart Manufacturing Systems (LISMS). In 2020, he is named among of the ‘20 most Influential Professors in Smart Manufacturing’ by the Society of Manufacturing Engineers (SME). He was recognised by Web of Science as a Clarivate™ Highly Cited Researcher in 2020.