The Topological Structure of Approximation Operators on a CCD Lattice
نویسندگان
چکیده
Rough sets deal with the vagueness and granularity in information systems. Reference[3] discusses rough approximations on a complete completely distributive lattice(CCD lattice for short) and brings generalizations of rough sets into a unified framework. This paper is devoted to the discussion of the relationship between approximations and topologies on a CCD lattice. It is proved that the set of all upper approximations (or of lower approximations) with respect to a partition consists of a clopen topology.
منابع مشابه
Categories of lattice-valued closure (interior) operators and Alexandroff L-fuzzy topologies
Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This ...
متن کاملThe Topological Properties of the Approximation Operators on A CCD Lattice
Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. Rough approximations on a complete completely distributive lattice(CCD lattice for short) and brings generalizations of rough sets into a unified framework are discussed in [3]. This paper is devoted to the discussion of the relationship between approximations and topologies on a CCD lattice. It ...
متن کاملTopological structure on generalized approximation space related to n-arry relation
Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...
متن کامل$L$-fuzzy approximation spaces and $L$-fuzzy topological spaces
The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces.
متن کاملOn generalized topological molecular lattices
In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices, topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009