To solve the multi-attribute decision making problems in Pythagorean fuzzy environment, a multi-attribute decision making method based on Pythagorean fuzzy Frank operator was proposed. Firstly, Pythagorean fuzzy number and Frank operator were combined to obtain the operation rule based on Frank operator. Then the Pythagorean fuzzy Frank operator was proposed, including Pythagorean fuzzy Frank weighted average operator and Pythagorean fuzzy Frank weighted geometric operator, and the properties of these operators were discussed. Finally, a multi-attribute decision making method based on Pythagorean fuzzy Frank operator was proposed, which was applied to an example of green supplier selection. The example analysis shows that the proposed method can be used to solve the actual multi-attribute decision making problems, and can be further applied to areas such as risk management and artificial intelligence.

In order to solve the dynamic evaluation problem of cloud computing security, a method named interval-valued hesitant fuzzy grey compromise relation analysis for accurately evaluating the security of cloud computing was proposed. Firstly, a new interval-valued hesitant fuzzy distance formula was defined to measure the distance between two interval-valued hesitant fuzzy sets. Then, two new interval-valued hesitant fuzzy normalization formulas were constructed to solve the different dimensions of attributes. Meanwhile, the concept of grey compromise relation degree was put forward to consider all the expert opinions and solve the situation when the attributes have conflicts. On the basis of this, a new interval-valued hesitant fuzzy grey compromise relation analysis method was presented to evaluate the security of cloud computing. The analysis results show that the proposed method is feasible, and its scientific and effective characters are proved by comparing with the existed interval-valued hesitant fuzzy multiple attribute decision making literatures.