Neutrosophic Matroids, Antimatroids, and Greedoids: A Unified Framework for Combinatorial Structures under Uncertainty

Abstract

A matroid is a combinatorial structure that extends the concept of linear independence from vector spaces to arbitrary sets. Matroids are widely applied in fields such as discrete optimization due to their rich mathematical properties and their applicability in areas like graph theory and computer science. Antimatroids and greedoids are well-known related concepts. To address uncertainty, the concept of fuzzy matroids was developed, extending matroid theory using fuzzy sets and serving as a subject of extensive study. This paper presents the mathematical definitions of neutrosophic matroids, neutrosophic antimatroids, and neutrosophic greedoids. These combinatorial structures extend classical concepts by incorporating neutrosophic sets, facilitating more advanced modeling of uncertainty and indeterminacy.