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Intuitionistic fuzzy sets theory is the modification or extension of fuzzy sets theory by incorporating two additional functions to the membership function. We studied the mathematics of intuitionistic fuzzy sets in collaboration with fuzzy sets. In terms of application, intuitionistic fuzzy sets theory is awesome because of its ability to cope with uncertainties in decision making especially in difficult cases we elaborated in this study. In a nutshell, intuitionistic fuzzy sets theory is a suitable and reliable tool in decision science.