Topological Spaces and Covering Rough Sets
نویسنده
چکیده
Rough set theory (RST) is a modern tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. One of the limitations of RST is its dependence on portioning the universe according to equivalence relation on the universe of objects in information systems. The purpose of this paper is to construct connections between generalized rough sets based on covering and the rough sets based on the topology whose sub base is the cover. Firstly, we present basic concepts and properties covering of rough sets. Then we give examples for topologies whose sub base is the cover, relationships between covering approximations and topological approximations are obtained and counter examples for inverse relationships are given. Rough membership function with respect to topology is constructed and compared with its correspondence.
منابع مشابه
Multigranulation single valued neutrosophic covering-based rough sets and their applications to multi-criteria group decision making
In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...
متن کاملStructure of Covering-based Rough Sets
Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringb...
متن کاملCovering Rough Sets From a Topological Point of View
—Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces are explored.
متن کاملOn topological covering-based rough spaces
Rough set theory, a mathematical tool to deal with vague concepts, has originally described the indiscernibility of elements by equivalence relations. Covering-based rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as subbase, neighborhood and separation axioms have bee...
متن کاملTOPOLOGICAL SIMILARITY OF L-RELATIONS
$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...
متن کامل