A Multi-attribute Decision Making Method Of Incomplete Dual Hesitant Fuzzy Sets

Multi-attribute decision making has a wide application in the real life of human and solves the problems of selecting the optimal alternative according to the evaluation values of each alternative attribute.In life,people often adopt two attitudes of supportiveness and opposition when they make judgments.The dual hesitant fuzzy set consists of two parts,that is,membership and non-membership.It is a powerful tool of dealing with the uncertain information and expressing both positive and negative information in the decision making process.In this paper,a multi-attribute decision making method based on incomplete dual hesitant fuzzy sets for the problem of information values missing is proposed.The main results are shown as follows:Firstly,the complementary method of incomplete dual hesitant fuzzy elements is proposed.According to the similarity of the traditional dual hesitant fuzzy sets,the similarity of incomplete dual hesitant fuzzy elements is proposed.The information values of incomplete dual hesitant fuzzy are complemented by the maximum similarity method: finding the maximum similarity between any of the two alternatives under the same attribute,filling the missing values to the alternatives of having the greatest similarity under the same attribute,until incomplete dual hesitant fuzzy elements turn into complete dual hesitant fuzzy elements.This method not only ensures the maximum similarity between any of the two alternative attribute values,but also solves the problem of missing information values.An example of network commodity evaluation shows the effectiveness and practicability of complementary method for the incomplete dual hesitant fuzzy information value based on maximum similarity.Then,a multi-attribute decision making method with unknown weights based on granular computing is proposed.Complementing dual hesitant fuzzy sets based on the complementary method of maximum similarity for incomplete similarity dual hesitant fuzzy sets,then a definition of greater than possibility degree of complete dual hesitant fuzzy elements is proposed and the preference matrix under corresponding attributes is constructed.The weight of each attribute is determined by calculating the preorder entropy and the similarity of the preorder granular structure corresponding to the fuzzy preference matrix.The method is applied to the instance of selecting the shop employee in the campus supermarket,which effectively solves the decision making problem that the weight unknown and avoids the subjectivity of human give weight.Finally,a decision method of incomplete dual hesitant fuzzy set with unknown weight based on the maximum deviation method is proposed.Based on the similarity of incomplete dual hesitant fuzzy given in the third section,the distance of the dual hesitant fuzzy elements is further proposed: the distance of incomplete dual hesitant fuzzy elements and the distance of complete dual hesitant fuzzy elements.Using the maximum deviation method to determine the unknown attribute weights solves the problem of unknown weight in multi-attribute decision making problems.Based on the TOPSIS and the distance of dual hesitant fuzzy elements,the optimal scheme is determined based on the distance by the positive or negative ideal schemes.An example of campus singing contests selection is given to illustrate the effectiveness of the decision making method based on the maximum deviation method for incomplete dual hesitant fuzzy sets.