Simplified interval-valued intuitionistic fuzzy integrals and their use in park siting

The interval-valued intuitionistic fuzzy sets have received great attention of researchers because they can comprehensively depict the characters of things. In the past few years, some scholars have investigated the calculus of intuitionistic fuzzy information, but yet there is no research on the integrals in interval-valued intuitionistic fuzzy circumstance. To fill this vacancy, in this paper, we shall focus on investigating the integrals of simplified interval-valued intuitionistic fuzzy functions (SIVIFFs) and give their application in group decision making. We first develop the indefinite and definite integrals of SIVIFFs, and study their characteristics in detail. Then we establish the relationship between these two classes of integrals by giving two Newton-Leibniz formulas for SIVIFFs. Finally, a practical example concerning the park siting problem is given to illustrate the application of simplified interval-valued intuitionistic fuzzy integrals.