Hesitant Fuzzy PROMETHEE ? Method And Its Application In Multi-attribute Decision Making

As a latest extension of fuzzy set,hesitant fuzzy set is an effective tool to deal with vagueness and uncertainty,and its researches are mainly applied to the field of multi-attribute decision making problems.Recently,various multi-attribute decision making methods have been studied under the environment of hesitant fuzzy information.However,these methods have its advantage and disadvantage,and need to be improved.In this paper,we combine the hesitant fuzzy set with PROMETHEE II method,introducing a novel multi-attribute decision making method-hesitant fuzzy PROMETHEE II method.The main content of the paper is stated as follows:(1)The core content of multi-attribute decision making is the ranking of hesitant fuzzy sets,while it is critical to extract some useful ranking index from hesitant fuzzy set.In this paper,centroid function,as an extension of score function of a hesitant fuzzy element in the process of ranking,is proposed.And we study some methods to construct"masses" of the centroid function,its property is also studied.In addition,the index used to describe the hesitancy of a hesitant fuzzy element is also important.So,the concordance function of a hesitant fuzzy element,as a new index,is proposed to depict the concordance degree of the membership degrees.In a word,these ranking indices are of great significance in the construction of the hesitant fuzzy decision making method.(2)The PROMETHEE II method considers the deviation of attribute values in dif-ferent alternatives,and all alternatives are fully compared.The core of this method is the construction of the preference function,and the construction of the preference function is based on the deviation of attribute values of alternatives.It is used to reflect the pref-erence degree of one alternative over another alternative on the same attribute.Since,the deviation of attribute values is a real number in PROMETHEE II method,while the deviation of attribute values is a hesitant fuzzy element in hesitant fuzzy decision making problems.Hence,we combine centroid function with concordance function,proposing the utility function of a hesitant fuzzy element,and we construct the preference function by the deviations of utility values.Finally,we propose a novel multi-attribute decision making method-hesitant fuzzy PROMETHEE ? menthod in the combination of the constructed preference function and PROMETHEE ? method.