Covering matroid

In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and can sometimes be more efficient to deal with problems in the real world. Through extending partitions to coverings, we propose a new type of matroids called covering matroids and prove them to be an extension of partition matroids. Secondly, since some researchers have successfully applied partition matroids to classical rough sets, we study the relationships between covering matroids and covering-based rough sets which are an extension of classical rough sets. Thirdly, in matroid theory, there are many special matroids, such as transversal matroids, partition matroids, 2-circuit matroid and partition-circuit matroids. The relationships among several special matroids and covering matroids are studied.Comment: 15 page

Geometric lattice structure of covering-based rough sets through matroids

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relationships. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by the covering, and its characteristics including atoms, modular elements and modular pairs are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, sufficient and necessary conditions for three types of covering upper approximation operators to be closure operators of matroids are presented. We exhibit three types of matroids through closure axioms, and then obtain three geometric lattice structures of covering-based rough sets. Third, these four geometric lattice structures are compared. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely geometric lattice, to study covering-based rough sets

More on neutrosophic soft rough sets and its modification

This paper aims to introduce and discuss anew mathematical tool for dealing with uncertainties, which is a combination of neutrosophic sets, soft sets and rough sets, namely neutrosophic soft rough set model. Also, its modification is introduced. Some of their properties are studied and supported with proved propositions and many counter examples

Topological and algebraic characterization of coverings sets obtained in rough sets discretization and attribute reduction algorithms

Abstract. A systematic study on approximation operators in covering based rough sets and some relations with relation based rough sets are presented. Two different frameworks of approximation operators in covering based rough sets were unified in a general framework of dual pairs. This work establishes some relationships between the most important generalization of rough set theory: Covering based and relation based rough sets. A structured genetic algorithm to discretize, to find reducts and to select approximation operators for classification problems is presented.Se presenta un estudio sistemático de los diferentes operadores de aproximación en conjuntos aproximados basados en cubrimientos y operadores de aproximación basados en relaciones binarias. Se unifican dos marcos de referencia sobre operadores de aproximación basados en cubrimientos en un único marco de referencia con pares duales. Se establecen algunas relaciones entre operadores de aproximación de dos de las más importantes generalizaciones de la teoría de conjuntos aproximados. Finalmente, se presenta un algoritmo genético estructurado, para discretizar, reducir atributos y seleccionar operadores de aproximación, en problemas de clasificación.Doctorad