Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making

• We investigate the MADM problems with hesitant triangular fuzzy information.
• We develop the definition and operations of the hesitant triangular fuzzy sets.
• We develop some hesitant triangular fuzzy Einstein aggregation operators.
• We utilize these operators to solve the hesitant triangular fuzzy MADM problems.

In this paper, we investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements and score function of hesitant triangular fuzzy elements are introduced. Then, we have developed some hesitant triangular fuzzy aggregation operators based on the Einstein operation: the hesitant triangular fuzzy Einstein weighted averaging (HTFEWA) operator, hesitant triangular fuzzy Einstein weighted geometric (HTFEWG) operator, hesitant triangular fuzzy Einstein ordered weighted averaging (HTFEOWA) operator, hesitant triangular fuzzy Einstein ordered weighted geometric (HTFEOWG) operator, hesitant triangular fuzzy Einstein hybrid average (HTFEHA) operator and hesitant triangular fuzzy Einstein hybrid geometric (HTFEHG) operator. We have applied the hesitant triangular fuzzy Einstein weighted averaging (HTFEWA) operator, hesitant triangular fuzzy Einstein weighted geometric (HTFEWG) operators to multiple attribute decision making with hesitant triangular fuzzy information. Finally an illustrative example has been given to show the developed method.