Abstract
Linguistic neutrosophic numbers (LNN) is presented by Fang and Ye in 2017, which can describe the truth, falsity, and indeterminacy linguistic information independently. In this paper, the LNN and the Bonferroni mean operator are merged together to propose a LNN normalized weighted Bonferroni mean (LNNNWBM) operator and a LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator and the properties of these two operators are proved. Further, multi-attribute group decision methods are introduced based on the proposed LNNNWBM and LNNNWGBM operators, and then an example is provided to demonstrate the application and validity of the proposed methods. In addition, in order to consider the effect of the parameters p and q on the decision results, different pairs of parameter values are employed to verify the decision results.
Highlights
In dealing with the complex, unknown, and uncertain decision-making problems, a group of decision-makers are usually employed to analyze a set of alternatives and to get the optimal result in a certain way
In this paper, the proposed decision-making methods based on the LNN normalized weighted Bonferroni mean (LNNNWBM) operator and the LNNNWGBM operator provide a new way for decision-makers under
MADGM methods based on the LNNNWGBM and LNNNWGBM operators for Linguistic neutrosophic numbers (LNN) are proposed in this paper
Summary
In dealing with the complex, unknown, and uncertain decision-making problems, a group of decision-makers are usually employed to analyze a set of alternatives and to get the optimal result in a certain way. Some methods for multiple attribute group decision-making (MAGDM) were proposed based on two-dimension uncertain linguistic variable [7,8]. Since the Bonferroni mean (BM) is a useful operator in decision-making [15], it was extended to hesitant fuzzy sets, IFSs, and interval-valued IFSs to propose their some Bonferroni mean operators for decision making [16,17,18,19,20]. Fang and Ye proposed the linguistic neutrosophic numbers (LNN) and their basic operational laws [21]. This paper proposes a LNN normalized weighted Bonferroni mean (LNNNWBM) operator, a LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator and their MAGDM methods.
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