The Decision Making For Interval-valued Hesitant Fuzzy Set Based On Outranking Relation

Fuzzy multiple attribute decision making (FMADM) theory is an important part of modern decision science. Compared with traditional multi-attribute decision making (MADM) methods,FMADM can better describe the complexity and fuzziness in the process of decision making.However, with the rapid development of society, the decision making problems are becoming more and more complicated, In response to the growing complexity of the decision making environment, various forms of expand fuzzy sets have been proposed. As one of extension form of the fuzzy set, interval-valued hesitant fuzzy set shows stronger ability to express fuzziness and uncertainty and so on. But as a new direction for. research, interval-valued hesitant fuzzy set needs to further perfection both in theoretical research or method application. Therefore, it is of great theoretical significance and practical value to carry out the research of multi-attribute decision making method with interval fuzzy sets. The main research works of this paper are as follows:(1) A new decision making method for ELECTRE based on interval-valued hesitant fuzzy set is proposedAiming at the decision making information being the interval-valued hesitant fuzzy set, the concepts of score function,possibility degree, deviation degree and distance measure of interval-valued hesitant fuzzy sets are introduced to construct the concordance sets, discordance sets and its corresponding indices , which can avoids the drawbacks of losing or distortion of the decision-makers' preference information. For the reason that the choice of threshold values of classical ELECTRE ? method is sensitive to the decision result, a modified version of the ELECTRE method is used to obtain the optimal alternative, and the proposed method is applied to an illustrative example to demonstrate its practicality and effectiveness.(2) A decision making method for PROMETHEE based on interval-valued hesitant fuzzy sets is proposedClassical PROMETHEE method decides the superiority of each two alternatives in terms of the difference between attribute values. Under the condition of the attribute information being interval-valued hesitant fuzzy sets, the score function of interval-valued hesitant fuzzy set and the possibility degree are introduced to construct precedence function, for the reason that decision-makers' preference to the alternatives is not always linear change or step change with the difference of attribute, a new priority function is proposed by extending the existing priority functions. Besides two types of triangle preference function are proposed motivated by the sine triangle function and cosine triangle function, then we prove the two triangle precedence functions are equivalent simultaneously. The precedence index of each pairs of alternatives is obtained by using the triangle precedence function, we obtain the ranking of alternatives by calculating each alternative's leaving flow, entering flow and net flow.