The q‐rung orthopair fuzzy sets (q‐ROFs) are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the membership degree and the qth power of the degrees of non‐membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the q‐rung orthopair fuzzy weighted averaging operator and the q‐rung orthopair fuzzy weighted geometric operator to deal with the decision information, and their some properties are well proved. Further, based on these operators, we presented two new methods to deal with the multi‐attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.
In the real multi‐attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q‐rung orthopair fuzzy sets (q‐ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non‐membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q‐rung orthopair fuzzy numbers (q‐ROFNs) to propose the q‐rung orthopair fuzzy BM (q‐ROFBM) operator, the q‐rung orthopair fuzzy weighted BM (q‐ROFWBM) operator, the q‐rung orthopair fuzzy geometric BM (q‐ROFGBM) operator, and the q‐rung orthopair fuzzy weighted geometric BM (q‐ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q‐ROFWBM and q‐ROFWGBM operators are very useful to deal with MAGDM problems.
In this paper, we proposed a single-valued neutrosophic normalized weighted Bonferroni mean (SVNNWBM) operator on the basis of Bonferroni mean, the weighted Bonferroni mean (WBM), and the normalized WBM. Firstly, the definition, operational laws, characteristics, and comparing method of single-valued neutrosophic numbers (SVNNs) are introduced. Then, the SVNNWBM operator is developed, and some properties and special cases of this operator are analyzed. Furthermore, an approach is developed to solve the multiple attribute decision-making problems with SVNNs based on the SVNNWBM operator. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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