Soft Computing

, Volume 22, Issue 3, pp 797–810 | Cite as

Multiple attribute decision-making method based on 2-dimension uncertain linguistic density generalized hybrid weighted averaging operator

  • Peide LiuEmail author
  • Fei Teng
Methodologies and Application


Two-dimension uncertain linguistic variables (2DULVs) are very effective tools in describing the uncertain and fuzzy information, which are composed of I class linguistic information and II class linguistic information. Density aggregation operators not only consider the importance of all attributes but also take the importance of the density and the order positions of attributes into account, so they can more accurately deal with the fuzzy decision-making problems. In this paper, firstly, some basic theories, such as the definition, the expectation value and the operational laws of the 2DULVs, are briefly introduced. Then, some density aggregation operators based on 2DULVs are proposed, such as 2-dimension uncertain linguistic density arithmetic aggregation operators, 2-dimension uncertain linguistic density geometric aggregation operators and 2-dimension uncertain linguistic density generalized aggregation operators. Furthermore, we propose a multiple attribute decision-making method based on the 2-dimension uncertain linguistic density generalized hybrid weighted averaging operators. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.


2-dimension uncertain linguistic variables Density aggregation operator Multiple attribute decision making Generalized hybrid weighted averaging operator 



This paper is supported by the National Natural Science Foundation of China (Nos. 71471172 and 71271124), the Special Funds of Taishan Scholars Project of Shandong Province, National Soft Science Project of China (2014GXQ4D192), Shandong Provincial Social Science Planning Project (No. 15BGLJ06), the teaching reform research project of undergraduate colleges and Universities in Shandong province (2015Z057) and the science and technology project of colleges and universities in Shandong Province (J13LN19). The authors also would like to express appreciation to the anonymous reviewers and Editors for their very helpful comments that improved the paper.

Compliance with ethical standards

Conflicts of interest

Disclosure of potential conflicts of interest. We declare that we do have no commercial or associative interests that represent a conflict of interests in connection with this manuscript. There are no professional or other personal interests that can inappropriately influence our submitted work.

Human participants

Research involving human participants and/or animals. This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina

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