Order Relations For Hesitant Fuzzy Sets And Its Application In Multi-attribute Decision Making

Multi-attribute decision making problems exist in every aspect of social life,it not only contains the strategic decisions about nation,such as China’s south-north water diversion project,the construct of three gorges dam,etc,but also covers the people’s daily routine,such as travel plans,the choice of financial product.The purpose of multi-attribute decision making problem is to select the best scheme from several schemes with the same attribute.Because of the complexity of decision problems and decision making environment,as well as ambiguity of human thinking,decision makers usually use interval numbers,triangular fuzzy numbers,trapezoidal fuzzy numbers,intuitionistic fuzzy numbers and hesitant fuzzy sets to describe uncertain decision information.However,hesitant fuzzy sets have the advantage of describing the uncertain decision information in the case of indecision,which can reflect the real situation of decision making,therefore,the research of multi-attribute decision making method in hesitant fuzzy environment is of great theoretical and practical significance.The main contents are as follows:(1)The order relation of hesitant fuzzy sets is the key to making decisions based on hesitant fuzzy decision making information.In this thesis,we begin with order relation of hesitant fuzzy sets,and analyze the drawbacks of the existing decision making techniques(including lack the flexibility,decision making information loss,etc.).In order to overcome these defects,new order relations between two hesitant fuzzy sets will be constructed----possibility degree and priority degree,and its properties will be studied(normative,complementarily and weak transitivity,etc).The new order relation can keep the integrity of decision information as much as possible and avoid the loss of decision information.(2)Based on the introduced order relation(possibility degree and priority degree)between two hesitant fuzzy sets in this thesis,some new multi-criteria decision making models will be proposed.Besides,the multi-attribute decision making methods based on the proposed order relation are compared with the traditional decision making technology to demonstrate its validity and rationality.(3)In the hesitant fuzzy linguistic environment,a new distance measure between two linguistic terms is proposed in this thesis,accordingly,the construction model of order relation between the fuzzy linguistic terms is developed,including Hamming distance,Euclidean distance and Hausdorff distance as well as for their promotion.What the research of multiple attribute decision making method under the hesitant fuzzy environment will be helpful to improve the theory of multiple attribute decision making and enrich the theory and method of uncertain decision making.