| Interval-valued intuitionistic fuzzy sets (IVIFS) are the extension of intuitionistic fuzzy sets. The membership degree and the non-membership degree of elements of IVIFS are represented as interval numbers. IVIFS have been widely applied owing to its powerful expression in describing fuzziness. Generally, interval-valued intuitionistic fuzzy multi-attribute decision making is attributed to the comparison of interval-valued intuitionistic fuzzy numbers (IVIFN), so domestic and foreign scholars have paid attention to the ranking method of IVIFN. In this thesis, the ranking method of intuitionistic fuzzy numbers (IFN) and IVIFN is mainly studied. The main contents and results are summarized as follows:(1) In order to obtain more information for comparison and ranking, a new accumulated score function and a new accumulated accuracy function of IFN are put forward on the basis of the method of accumulation and limitation which deeply excavates the uncertain information of IFN. Then, a new ranking method of IFN is given. Furthermore, the proposed method is extended to IVIFN. A new accumulated score function and a new accumulated accuracy function of IVIFN both are presented, and a new ranking method of IVIFN is also given.(2) The geometric features of IFN are analyzed based on the space geometric description of IFN. A geometric ranking index is provided according to some geometric quantities which reflect the inferiors and superiors of IFN. Then, a new ranking method of IFN is given. Meanwhile, the concept of geometric ranking index is expended to IVIFN. A geometric ranking index of IVIFN is proposed by considering the geometric quantities which reflect the inferiors and superiors of IVIFN, and a new ranking method of IVIFN is also given. |
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