Simplified interval-valued intuitionistic fuzzy sets with intuitionistic fuzzy numbers

There has been a growing interest and activity in the field of interval-valued intuitionistic fuzzy sets (IVIFSs). It is generally useful to express the variations of the membership function and the non-membership function in fuzzy circumstances. However, the IVIFS is a little bit complicated on expressions and calculations. To overcome this limitation, this paper aims to introduce a succinct way to define IVIFS by two intuitionistic fuzzy numbers (IFNs), and thus, a simplified interval-valued intuitionistic fuzzy number (SIVIFN) is proposed. Afterwards, a series of operational laws and aggregation techniques over the SIVIFNs are developed, and their desirable properties are investigated in detail, which enrich the interval-valued intuitionistic fuzzy set theory. Finally, a numerical example is provided to illustrate the straightforward expressions and calculations of the SIVIFNs.