Necessary and sufficient condition for the existence of Atanassov's Intuitionistic Fuzzy based additive definite integral

Abstract

Atanassov came up with an idea of the intuitionistic fuzzy set (AIFS), primarily a generalized extension of Zadeh's fuzzy set. AIFS is more supple in tackling the real world's unpredictability rather than Zadeh's fuzzy set. The researchers from various disciplines are attracted to the AIFS because of its proximity to real life. AIFS is very rich in literature in both aspects, i.e., theoretical and practical. At present, the intuitionistic fuzzy integral is a scorching issue of the AIFS. Furthermore, to aggregate and process the data, the existence of integral is compulsory. It is reasonably necessary to look that whether integral exists or not for the given data. Thus, our primary aim is to confirm the existence of a given additive definite integral (ADI). We have provided a necessary and sufficient condition to prove the existence of the given ADI. Finally, an example is fabricated for application grounds. It is shown that to aggregate a vast amount of data aggregation operator prompted from ADI is an outstanding option.