On the Equivalence of Bounded Multigroups and Discrete Fuzzy Subgroups

In this note, we establish a formal equivalence between the bounded multigroup structures introduced by Nazmul et al. the class of fuzzy subgroups defined by Rosenfeld, when restricted to discrete membership values of the form [Formula: see text] where [Formula: see text]. By introducing a normalization map [Formula: see text] that links multigroup counts with fuzzy membership degrees, we prove that every multigroup in the bounded multiset space [Formula: see text] corresponds bijectively to a discrete [Formula: see text]-fuzzy subgroup, and conversely. Several propositions from Nazmul et al. are reformulated within the fuzzy framework, showing that these results emerge as immediate corollaries of standard fuzzy subgroup theory. This analysis highlights the mathematical overlap between the two approaches and clarifies that much of the multigroup terminology amounts to a reformulation rather than a genuine extension of fuzzy algebra.