Abstract
To objectively evaluate the influence of hesitant fuzziness on the ranking of alternatives in multi-attribute decision making with hesitant fuzzy or probabilistic hesitant fuzzy information, the binary connection number of set pair analysis is applied to hesitant fuzzy multi-attribute decision making. The hesitant or probabilistic hesitant fuzzy set is transformed to the binary connection number. A hesitant fuzzy multi-attribute decision making model based on binary connection number is then established. Binary connection number theory is utilized to obtain the hesitant fuzzy center and decision-making suggestions about the alternative ranking under different hesitant fuzzy conditions. Experimental examples show that the hesitant fuzzy multi-attribute decision making model based on binary connection number has a certain versatility. It can determine the optimal scheme under the influence of hesitant fuzziness on the alternative ranking and contains the results of the same hesitant fuzzy decision-making problem using other methods, which helps in targeted decision making according to different hesitant fuzzy conditions.
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