Abstract
When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.
Highlights
The multiple attribute decision making (MADM) problem is a significant area of decision science, whose theories and methods are widely used in engineering, economics, management, the military and many other fields
We present a detailed formula as an example to introduce the P2TLMSM operator in the context MADM
We present a detailed formula as an example to introduce the P2TLMSM operator in the context of MADM
Summary
The multiple attribute decision making (MADM) problem is a significant area of decision science, whose theories and methods are widely used in engineering, economics, management, the military and many other fields. Qin and Liu [14] proposed several operators based on 2-tuple linguistic information and the Muirhead mean (MM) operator It is known as a mean type aggregation operator that can utilize the intact relation between the multi-input parameters. Wang et al [31] extended MSM aggregation operators with single-valued neutrosophic linguistic variables and developed methods for multiple-criteria decision making (MCDM). Liu and Zhang [33] extended MSM operators with the single-valued trapezoidal neutrosophic number (SVTNNs) to account for the correlation between multi-input arguments and conveniently depict uncertain information in the decision making process. We use the picture 2-tuple linguistic set based on PFS and 2-tuple linguistic information to address MADM problems, thereby overcoming the above limitation and preventing loss of information in the calculation and aggregation processes.
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