Multi-Universe Frameworks for Fuzzy, Neutrosophic, Soft, and Rough Sets

An uncertain set assigns to each element a generalized uncertainty value and thus provides a unified formal language encompassing fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and other related degree-based models. In most existing frameworks, a single universe of discourse is fixed in advance, and the associated structures and properties are studied within that single universe. In this paper, we introduce the notion of a multi-universe set, in which multiple universes of discourse are considered simultaneously. Within this framework, we define multi-universe fuzzy, neutrosophic, soft, and rough sets, and examine their fundamental properties.