Generalized fuzzy sets and their applications in purchase satisfaction, personnel posting and disease diagnosis

Abstract

We introduce a new class of sets called the generalized fuzzy sets as a generalization of fuzzy, intuitionistic fuzzy and the Pythagorean fuzzy sets. Together with their basic and important properties, we define the relations and distances on them. We demonstrate their importance by making their comparisons with other fuzzy sets available in the literature. We implement the idea of these sets on the examples in the fields of purchase satisfaction, personnel posting and disease diagnosis. By the comparison of their results with the results available in the literature, we suggest that this new category of sets is a more summarized form of all the fuzzy sets presented up to date, and has a wider scope of applications as compared to other fuzzy sets. The generalized fuzzy sets will entertain more applications than other sets.