@article{Alali2026, 
author = {Amal S. Alali and Ravi Kumar Bandaru and Seok-Zun Song and Young Bae Jun},
title = {Fuzzy GE-norms and fuzzy normed GE-algebras},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4243-4262},
keywords = {GE-algebra, fuzzy GE-norm, transitivity, GE-morphism, fuzzy convergence},
url = {https://www.sciopen.com/article/10.3934/math.2026170},
doi = {10.3934/math.2026170},
abstract = {In this paper, we introduce the notion of a fuzzy GE-norm on a GE-algebra    (                    X              ,      ∗    ,      1                                        X                                ) as a scale-dependent fuzzy analogue of the GE-norm introduced in [2]. We established fundamental structural properties of fuzzy GE-norms, derived several identities and generalizations of classical norm inequalities, and developed examples demonstrating the variety of fuzzy behaviors that arise in GE-algebraic settings. Particular attention was given to the interaction between fuzzy GE-norms and GE-morphisms. We showed that a fuzzy GE-norm is not automatically preserved under mappings induced by a GE-morphism. Positive preservation results were obtained when the morphism is injective or surjective and satisfies natural compatibility requirements. A central result of the paper is a complete characterization of fuzzy normability: a GE-algebra admits a fuzzy GE-norm if and only if its induced order is transitive. This theorem identifies transitivity as the precise structural requirement for norm-like behavior in GE-algebras. Additional results include uniqueness of fuzzy limits in commutative GE-algebras, continuity of left and right translations, fuzzy convergence criteria, and Lipschitz-type estimates for the rational fuzzy GE-norm.}
}