Journal of Systems Engineering and Electronics ›› 2017, Vol. 28 ›› Issue (6): 1152-1161.doi: 10.21629/JSEE.2017.06.13

• SYSTEMS ENGINEERING • Previous Articles     Next Articles

Cartesian product over interval valued intuitionistic fuzzy sets

Jianming Xie* and Sanyang Liu   

  1. School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
  • Online:2017-12-27 Published:2017-12-27

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Abstract:

The intuitionistic fuzzy set (IFS) based on fuzzy theory, which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set (IVIFS). On the basis of fuzzy set (FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS. In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored. We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs. 

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