Advanced fuzzy set theory is mostly used in real-time applications such as medical, satellite and agricultural field (Rani and Amsini 2019). In 1975, Zadeh pioneered another advanced fuzzy set called type II fuzzy set. Obviously, membership functions were defined by an expert based on his or her knowledge. These fuzzy set theories were applied to images that were poorly illuminated. The objects were barely visible in those images and furthermore uncertainties occurred. Type II fuzzy sets are the fuzzy sets for which the membership function is not a solitary value, meaning that every constituent is an interval.
A type II fuzzy set may be written as Atype2 = {x,μA (x) | xεX}, where μA(x) is the type II membership function. An interval-based type II fuzzy set is distinct with its upper and lower membership values and practically represented as μupper = [μ(x)]α; μlower = [μ(x)]1/α. The type II fuzzy set considers the fuzzy membership function as fuzzy. The uncertainty is corresponding to upper and lower levels of the membership function. A lot of authors suggested that fuzzy set theory is superior in obtaining better results with precise values for better-quality analysis. Fuzzy set theory helps to improve the accuracy and reduces error due to oscillation. Much research is going on advanced fuzzy set theories such as mathematical modeling and robotics.
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