A Fuzzy Signature Algebra Framework for Hierarchical Data Aggregation in Marine Monitoring Systems

Abstract

The algebraic structure of fuzzy signatures with the algebraic product and the algebraic sum operators is investigated. Given a rooted tree G_s = (V,E) and an associated set of aggregation operators AS, we prove that the family of fuzzy signatures F(G_s ,A_s ), equipped with the algebraic product (∗) and algebraic sum (+), forms a bounded lattice by verifying the commutativity, the associativity, and the absorption laws. As an application, we demonstrate
that this algebraic structure provides a principled and scalable mechanism for hierarchical data aggregation in marine monitoring systems, where sensor uncertainty, incomplete measurements, and multi-level decision hierarchies are effectively managed.