Interval-valued intuitionistic fuzzy aggregation operators |
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| Authors: | Weize Wang Xinwang Liu Yong Qin |
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| Affiliation: | [1]School of Economics and Management, Southeast University, Nanjing 210096, E R. China [2]State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, P. R. China |
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| Abstract: | The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making. |
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| Keywords: | interval-valued intuitionistic fuzzy set （IVIFS） interval-valued intuitionistic fuzzy weighted averaging （IVlFWA） operator interval-valued intuitionistic fuzzy ordered weighted averaging （IVI-FOWA） operator multiple criteria decision making （MCDM） mono-tonicity |
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