Hesitant bipolar fuzzy aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problems based on the aggregation operators with hesitant bipolar fuzzy information. Then, motivated by the ideal of arithmetic and geometric operation, we have developed some aggregation operators for aggregating hesitant bipolar fuzzy information: hesitant bipolar fuzzy weighted average (HBFWA) operator, hesitant bipolar fuzzy weighted geometric (HBFWG) operator, hesitant bipolar fuzzy ordered weighted average (HBFOWA) operator, hesitant bipolar fuzzy ordered weighted geometric (HBFOWG) operator, hesitant bipolar fuzzy hybrid average (HBFHA) operator and hesitant bipolar fuzzy hybrid geometric (HBFHG) operator. Then, we have utilized these operators to develop some approaches to solve the hesitant bipolar fuzzy multiple attribute decision making problems. Finally, an illustrative example for evaluating the constructional engineering software quality is then analyzed to illustrate the relevance and effectiveness of the proposed methodology.