Journal of Intelligent Manufacturing

, Volume 28, Issue 3, pp 625–632 | Cite as

Uncertain programming model for uncertain minimum weight vertex covering problem

  • Lin Chen
  • Jin PengEmail author
  • Bo Zhang
  • Shengguo Li


In this paper, the minimum weight vertex covering problem with uncertain vertex weights is investigated. By virtue of the uncertainty distribution operation of independent uncertain variables, the uncertainty distribution of the minimum weight of vertex cover is derived, and the concept of the \(\alpha \)-minimum cover among uncertain weight vertex covers is proposed within the framework of uncertain programming. Then an \(\alpha \)-minimum model for uncertain weight vertex covering problem is established and discussed. Taking advantage of some properties of uncertainty theory, the model can be transformed into the corresponding deterministic form. At last, a numerical example is presented to show the performance of the model.


Vertex covering problem \(\alpha \)-minimum cover \(\alpha \)-minimum model Uncertainty theory Uncertain programming 



This work is supported by the Projects of the Humanity and Social Science Foundation of Ministry of Education of China (No.13YJA630065), the Key Project of Hubei Provincial Natural Science Foundation (No.2012FFA065), the Scientific and Technological Innovation Team Project (No.T201110) of Hubei Provincial Department of Education, China, and the Fundamental Research Funds for the Central Universities (No. 31541411209).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.College of Mathematics and ScienceShanghai Normal UniversityShanghaiChina
  2. 2.Institute of Uncertain SystemsHuanggang Normal UniversityHubeiChina
  3. 3.School of Statistics and MathematicsZhongnan University of Economics and LawHubeiChina

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