Abstract
For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle. Moreover, the proposed operators do not take into account the correlation between any aggregation arguments. In order to overcome the deficiencies of the existing ranking method, based on the nonnegative normal neutrosophic number, this paper redefines the score function, the accuracy function, and partial operational laws. Considering the correlation between any aggregation arguments, the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator were investigated, and their properties are presented. Here, these two operators are applied to deal with a multiple attribute decision making problem. Example results show that the proposed method is effective and superior.
Highlights
During the decision making process, the evaluation information given by decision makers is often incomplete, indeterminate, and inconsistent
In order to avoid the disadvantages of the ranking, we propose the nonnegative normal neutrosophic number (NNNN)
We extend the DGWBGM to NNNNs and propose the dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean (DGNNNWGBM) operator
Summary
During the decision making process, the evaluation information given by decision makers is often incomplete, indeterminate, and inconsistent. Wang and Li [32,33] and Wang et al [34] developed some intuitionistic normal aggregation operators and proposed some MADM methods based on these operators, while. Liu [39,40,41] developed Frank operators, generalized weighted power averaging operators, and Heronian mean operators for application with NNN; Şahin [42] introduced generalized prioritized aggregation operators with NNN These operators do not consider the relationship between attributes. Some generalized aggregation operators are developed, which are the dual generalized nonnegative normal neutrosophic weighted. Bonferroni mean (DGNNNWBM) operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean (DGNNNWGBM) operator.
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