Definite integrals for aggregating continuous interval-valued intuitionistic fuzzy information

Atanassov's interval-valued intuitionistic fuzzy set (A-IVIFS), as an extension of Atanassov's intuitionistic fuzzy set (A-IFS), uses the membership function and the non-membership function to generate interval values to describe things' characteristics. To simplify the expression of interval-valued intuitionistic fuzzy number (IVIFN), the concept of simplified interval-valued intuitionistic fuzzy number (SIVIFN) is proposed. Recently, some experts have proposed a series of ways to fuse Atanassov's interval-valued intuitionistic fuzzy information. However, we find that those techniques can't aggregate those IVIFNs that spread all over a region. So in this paper, we try to find a new technique to solve the above-mentioned issue. Firstly, based on SIVIFNs, we propose the interval-valued intuitionistic fuzzy definite integral, analyze its properties and construct the relation between the proposed definite integral of SIVIFNs and that of IFVs proposed by previous researches, and then, based on the definite integral, we construct an interval-valued intuitionistic fuzzy definite integral (IIFDI) operator. Next, a technique is proposed to aggregate amounts of SIVIFNs by statistical methods. At last, an example about satisfaction evaluation of patient on medical system in China is given to show the effectiveness and practicability of our technique.