Relationships Between Two Types of Intuitionistic Fuzzy Definite Integrals

Intuitionistic fuzzy numbers (IFNs) are the basic components of Atanassov's intuitionistic fuzzy sets, which are very convenient and comprehensive in depicting the fuzzy characters of things in real life. In the existing literature, there are mainly two different types of definite integrals with respect to IFNs, which were developed from completely different aspects. The main purpose of this paper is to demonstrate their relationships in detail by deriving the definite integrals of two novel intuitionistic fuzzy functions. It is worth pointing out that one of the two types of definite integrals is shown to be a special case of another one, and finally, we also derive some other useful results for intuitionistic fuzzy calculus based on the division derivative.