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Fuzzy set is a modern tool for depicting uncertainty. This paper introduces the concept of fuzzy sub e-group as an extension of fuzzy subgroup. The concepts of identity and inverse are generalized in fuzzy sub e-groups. Every fuzzy subgroup is proven to be a fuzzy sub e-group, but the converse is not true. Various properties of fuzzy sub e-groups are established. Moreover, the concepts of proper fuzzy sub e-group and super fuzzy sub e-group are discussed. Further, the concepts of fuzzy e-coset and normal fuzzy sub e-group are presented. Finally, we describe the effect of e-group homomorphism on normal fuzzy sub e-groups.

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α, β)-Pythagorean fuzzy set is a very efficient way for dealing with uncertainty. In this article, we introduce the notions of (α, β)-Pythagorean fuzzy subring and (α, β)-Pythagorean fuzzy ideal of a ring. Further, we briefly describe various results related to it. Also, we discuss level subring of an (α, β)-Pythagorean fuzzy subring. Moreover, we study the direct product and ring homomorphism of (α, β)-Pythagorean fuzzy subring.INDEX TERMS (α, β)-PFS, (α, β)-PFSR, (α, β)-PFID, (α, β)-PFLSR