Abstract
A matroidal structure that generalizes the properties of independence. Relevant applications are found in graph theory and linear algebra. This paper will focus on the definitions of a matroid in terms of generalization for a crisp set called soft-set and soft-point, also we give some results related to this concept. A soft-matroid is defined and examples of soft-systems which form are given. The novel concept of independent soft-set is introduced. The notion maximal of independent soft-sets and minimal dependent soft-sets, with examples from linear algebra and soft-graph theory, are illustrated. Finally, we investigate some fundamental properties of soft-matroid.
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