Hesitant triangular fuzzy information aggregation in multiple attribute decision making

In this paper, we investigate the hesitant fuzzy multiple attribute decision making with incomplete weight information. An optimization model based on the maximizing deviation method, by which the attribute weight can be determined, is established. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the hesitant fuzzy weighted averaging (HFWA) operator to aggregate the hesitant fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effective. 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: the hesitant triangular fuzzy weighted averaging (HTFWA) operator, hesitant triangular fuzzy weighted geometric (HTFWG) operator, hesitant triangular fuzzy ordered weighted averaging (HTFOWA) operator, hesitant triangular fuzzy ordered weighted geometric (HTFOWG) operator, hesitant triangular fuzzy hybrid average (HTFHA) operator and hesitant triangular fuzzy hybrid geometric (HTFHG) operator. We have applied the hesitant triangular fuzzy weighted averaging (HTFWA) operator, hesitant triangular fuzzy weighted geometric (HTFWG) operators to multiple attribute decision making with hesitant triangular fuzzy information. Finally an illustrative example has been given to show the developed method.