Abstract
Abstract Fermatean fuzzy sets (FFSs) are invented to resolve the underlying limitations of intuitionistic fuzzy sets and Pythagorean fuzzy sets. The major goal of this study is to introduce Fermatean fuzzy semi-prime ideals of ordered semigroups. Fermatean fuzzy semi-prime ideals and Fermatean fuzzy prime ideals are introduced. Also, we illustrate some novel concepts to construct Fermatean fuzzy intra-regular and regular ideals. Using the conception of function of the characteristic of ordered semigroups of FFSs, we show certain fundamental facts. Several relations are given for the family of Fermatean fuzzy regular ideals of ordered semigroups.
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