MetaFuzzy, MetaNeutrosophic, MetaSoft, and MetaRough Set

Abstract

A MetaStructure is a higher-level framework treating collections of structures as objects, with natural operations that preserve isomorphisms across domains. An Iterated MetaStructure recursively applies the MetaStructure construction, forming successive layers in which structures of structures create deeper, hierarchical meta-levels. Concepts in the real world can be captured in terms of such meta-structures, and meta-level viewpoints are in fact applied in many different fields. Therefore, research on metastructures is important, but it has not yet been well developed in the areas of fuzzy sets and neutrosophic sets. To address this gap, in this paper, we define the MetaFuzzy Set, MetaNeutrosophic Set, Meta Soft Set, and MetaRough Set by extending fuzzy sets, neutrosophic sets, soft sets, and rough sets through the use of Meta Structure and Iterated Meta Structure.

J. Bangladesh Acad. Sci. 50(1); 107-145: March 2026