4.6 Article

Multicriteria Decision Making With Incomplete Weights Based on 2-D Uncertain Linguistic Choquet Integral Operators

Journal

IEEE TRANSACTIONS ON CYBERNETICS
Volume 51, Issue 4, Pages 1860-1874

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2019.2913639

Keywords

Linguistics; Frequency modulation; Decision making; Indexes; Cybernetics; Economics; Reliability; 2-D uncertain linguistic variable (2DULV); Choquet integral; fuzzy measure (FM); generalized Shapley index (GSI); multicriteria decision making

Funding

  1. National Natural Science Foundation of China [71771140, 71471172]
  2. Special Funds of Taishan Scholars Project of Shandong Province [ts201511045]
  3. Ministry of Science and Technology, Republic of China [MOST 107-2221-E-011-122-MY2]

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This paper proposes two novel MCDM methods, introduces some new operational laws of 2DULVs and four operators capturing criteria interactions, establishes models to obtain criteria weights, and explains the methods through examples, with comparative experimental results highlighting the superiorities of the approaches.
In regard to multicriteria decision making (MCDM) problems where the values of the criteria are expressed by 2-D uncertain linguistic variables (2DULVs), where the criteria are interactive and the criteria weights are incompletely known, two novel MCDM methods are proposed in this paper. First, we offer some novel operational laws of 2DULVs, which can avoid the operational results exceeding the boundary of linguistic term sets. Then, we propose four operators to capture the interactions over the criteria, namely, the 2-D uncertain linguistic Choquet averaging (2DULCA) operator, the 2-D uncertain linguistic Choquet geometric (2DULCG) operator, the Shapley 2DULCA (S2DULCA) operator, and the Shapley 2DULCG (S2DULCG) operator. In addition, we establish the models based on the maximization deviation approach and the Shapley function to get the criteria weights. Finally, we propose two novel MCDM methods under 2-D uncertain linguistic environments, where four examples are used to explain the created MCDM methods. Comparative experimental results are presented to highlight the superiorities of the created approaches.

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