Existence of Atanassov’s Intuitionistic Fuzzy Definite Integrals

Atanassov’s intuitionistic fuzzy set (A-IFS) is a more general form of Zadeh’s fuzzy set, and it is defined to deal with the uncertainty more accurately. The closeness of A-IFS to the reality attracted researcher from multidisciplinary areas. Regarding A-IFS, a lot of work has been done in both: theoretical and practical aspects. Nowadays, intuitionistic fuzzy integrals is a very hot topic of Atanassov intuitionistic fuzzy (A-IF). Moreover, the existence of the integral is essential to define aggregation operator and process the information, that is, necessary to check whether for a given data, the desired integral exists or not. Therefore, in this paper, our main focus will be to ensure the existence of the additive definite integrals (ADI). To do so, we will use bounded variation based functions (BV function), that are the functions whose approximate length are finite. Finally, we have constructed an example for application purpose and have shown that aggregation operator induced from ADI with BV function is a excellent choice to aggregate a huge amount of data.