Journal of Frontiers of Computer Science and Technology ›› 2022, Vol. 16 ›› Issue (8): 1898-1909.DOI: 10.3778/j.issn.1673-9418.2103009

• Theory and Algorithm • Previous Articles     Next Articles

Hierarchical Multi-attribute Decision-Making Method with Twofold Integral Operator of Cloud Model

WANG Tiedan, ZHANG Yuqing, PENG Dinghong()   

  1. Institute of Quality Development, Faculty of Management and Economics, Kunming University of Science and Technology, Kunming 650093, China
  • Received:2021-03-03 Revised:2021-05-31 Online:2022-08-01 Published:2021-06-09
  • About author:WANG Tiedan, born in 1971, senior engineer. His research interest is fuzzy decision methods.
    ZHANG Yuqing, born in 1996, M.S. candidate. Her research interest is fuzzy decision methods.
    PENG Dinghong, born in 1982, Ph.D., professor. His research interests include system engineering and fuzzy decision analysis.
  • Supported by:
    the National Natural Science Foundation of China(71861018);the National Natural Science Foundation of China(61364016);the Philosophy and Social Science Planning Programs of Yunnan Province(YB2019067);the Postdoctoral Science Foundation of China(2015T80990)


王铁旦, 张雨晴, 彭定洪()   

  1. 昆明理工大学 管理与经济学院 质量发展研究院,昆明 650093
  • 通讯作者: +E-mail:
  • 作者简介:王铁旦(1971—),男,云南昆明人,高级工程师,主要研究方向为模糊决策法。
  • 基金资助:


Due to the complexity of the actual decision-making problem, most indicators have the characteristics of mutual dependence. Therefore, for the multi-attribute decision-making problem with correlation between indicators under uncertain environment, a decision method with hierarchical structure as the framework and cloud model twofold integral (C-TI) as the aggregation operator is proposed. Firstly, in order to reflect the uncertain thinking of decision makers in determining the index weights, a cloud model fuzzy measure is proposed. Secondly, the cloud model twofold integral operator is constructed on the basis of cloud model fuzzy measure, which takes the cloud model as the representation of decision information, fully reflects the fuzzy and random nature of decision information. And twofold integral combining the advantages of Choquet integral and Sugeno integral is applied to aggregating the index values, which can not only effectively deal with the interaction problem between indexes, but also take into account the focus relationship between the index value and the weight. Subsequently, the theorems and properties of the cloud model twofold integral operator and the variation form of specific conditions are then discussed and the corresponding proofs are given. Finally, a hierarchical multi-attribute decision making method for cloud model twofold integral operator is constructed and applied to the corporate social responsibility assessment problem. Compared with other models, it is further shown that the method constructed in this paper is suitable for dealing with fuzzy and stochastic uncertainty problems and can take into account the overall decision effect while the indicators are correlated.

Key words: cloud model, twofold integral, aggregation operator, fuzzy measure, hierarchical multi-attribute decision making



关键词: 云模型, 双重积分, 聚合算子, 模糊测度, 层次多属性决策

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