| The theories of intuitionistic fuzzy set (IFS) and interval-valued intuitionis-tic fuzzy set (IVIFS) are the important theoretical foundations in the field of fuzzy multi-criteria decision making (FMADM). It usually requires us to rank intuitionistic fuzzy numbers (IFNs) or interval-valued intuitionistic fuzzy num-bers (IVIFNs) in a fuzzy decision making process. This thesis mainly focuses on the study about ranking methods of intuitionistic fuzzy numbers and inter-val-valued intuitionistic fuzzy numbers. The main contents and achievements are showed as follows:(1) In order to handle the ranking problems of IFNs, a new method for ranking IFNs has been proposed by establishing the relative ratio score function and the relative ratio accuracy function in this thesis. In addition, aim at reduc-ing the uncertain information of IFNs, new membership degree and new non-membership degree with more information are obtained by excavating the hesitation degree according to the herd mentality and decision maker’s risk-attitude. Then, the new IFNs are presented. And another ranking method of new IFNs based on the relative ratio score function and the relative ratio accu-racy function is given.(2) Methods for ranking IVIFNs are studied in this thesis. Due to the deci-sion maker as an important part in a fuzzy decision making process, a parameter which reflects the decision maker’s risk-attitude is introduced for converting in-terval-valued intuitionistic fuzzy numbers to parametric intuitionistic fuzzy numbers. And according to the methods of IFNs which have been proposed based on the relative ratio score function and the relative ratio accuracy function in this thesis, new ranking methods of IVIFNs are proposed. Moreover, some examples are also given to show the feasibility and effectiveness of IVIFNs’ ranking methods. |
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