Multiple Attribute Decision Making Method Based On Interval Probabilistic Hesitant Fuzzy Linguistic Term Sets

The multiple attribute decision making problem is an important research content in the decision making field and has a wide range of application prospects.In the multiple attribute decision making process,because of the complexity and fuzziness of the actual problem,it is difficult for the decision maker to give an accurate numerical value as the evaluation value of the attribute.The language information is often used to represent the evaluation values of attributes,such as "good","general" or "difference".Therefore,linguistic multiple attribute decision making,that is,the evaluation value of attributes is language value,and has become a hot topic of multiple attribute decision making.In practical applications,on the one hand,due to the incompleteness or uncertainty of information,decision makers may hesitate between several linguistic terms when evaluating the decision object according to attributes.ie,the decision makers provide hesitant fuzzy linguistic term sets to evaluate object.On the other hand,combined with the decision maker's knowledge backgroun,language habits,etc.,the decision maker gives preference or importance to hesitant linguistic terms.In this paper,a method of hesitant fuzzy multiple attribute decision making with an important degree is studied.The main contents are as follows:(1)Using the interval probabilistic to indicate the degree of importance,propose the interval probabilistic hesitant fuzzy linguistic term sets.The algorithm of interval probabilistic hesitant fuzzy linguistic term sets and the normalization of interval probabilistic hesitant fuzzy linguistic term sets are given.The score function and dispersion of interval probabilistic hesitant fuzzy linguistic term sets are proposed and used to compare the interval probabilistic hesitant fuzzy linguistic term sets.(2)The aggregation operators of interval probabilistic hesitant fuzzy linguistic term sets are studied,including weighted aggregation operators,power aggregation operators,ordered weighted power aggregation operators,and the properties of the aggregation operators are proved.By defining the distance between interval probabilistic hesitant fuzzy linguistic term sets,the degree of support in the power aggregation operator and the ordered weighted power aggregation operator is obtained.(3)A multiple attribute decision making method based on interval probabilistic hesitant fuzzy linguistic term sets aggregate operators is proposed and the specific decision steps are given.Applying the TOPSIS method to the interval probabilistic hesitant fuzzy linguistic environment,an extended TOPSIS method based on the interval probabilistic hesitant fuzzy linguistic set is proposed and the specific decision steps are given.The validity of the given method was verified by examples.In addition,in the case analysis,a method of transforming linguistic multiple attribute group decision making problem into interval probabilistic hesitant fuzzy linguistic multi-attribute decision making problem is also proposed.