Search results for "Rough set"
showing 10 items of 25 documents
Extensions and intentions in the rough set theory
1998
Abstract The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension. It is different from the well-known approaches in the literature in that the upper approximations and the lower approximations of ‘unknown’ sets are considered as certain families of ‘known’ sets. This approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets. The basic results presented in this paper, based on certain ideas of the second author, were formulated by the first author in his doctoral dissertation prepared under the su…
On Rough Sets in Topological Boolean Algebras
1994
We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.
Upper and lower approximations of general aggregation operators based on fuzzy rough sets
2015
Our paper deals with constructions of upper and lower general aggregation operators which act on fuzzy sets. These constructions are based on fuzzy rough sets and provide two approximations (upper and lower) of the pointwise extension and the t-extension of an ordinary aggregation operator. Considering two lattices of corresponding general aggregation operators we describe two approximate systems with respect to a lattice of fuzzy equivalence relations.
Innovation Dynamics in Space: Local Actors and Local Factors
1997
This paper addresses the issue of technogenesis and its geographical pattern. It aims to offer both a general analysis framework and a test on innovation data from several European cities. This framework is mainly built on the product life-cycle and the incubation approach. On the basis of this framework, it is argued that the phases of an industrial life-cycle have several firm-specific effects. First, these phases influence innovativeness and thus profit levels, output and employment of firms in a spatially distinct way. Second, the phases of the life-cycle mirror the importance of local factors for innovations, and third, they affect strategic decisions of firms, inter alia by influencin…
Towards the theory of M-approximate systems: Fundamentals and examples
2010
The concept of an M-approximate system is introduced. Basic properties of the category of M-approximate systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximate systems.
An Improved Decision System for URL Accesses Based on a Rough Feature Selection Technique
2015
Corporate security is usually one of the matters in which companies invest more resources, since the loss of information directly translates into monetary losses. Security issues might have an origin in external attacks or internal security failures, but an important part of the security breaches is related to the lack of awareness that the employees have with regard to the use of the Web. In this work we have focused on the latter problem, describing the improvements to a system able to detect anomalous and potentially insecure situations that could be dangerous for a company. This system was initially conceived as a better alternative to what are known as black/white lists. These lists co…
Rough Pragmatic Description Logic
2013
In this chapter, a rough description logic is built on the basis of a pragmatic standpoint of representation of knowledge. The pragmatic standpoint has influenced the acceptance of a broader definition of the semantic network than that appearing in the literature. The definition of the semantic network is a motivation of the introduced semantics of the language of the descriptive logic. First, the theoretical framework of representation of knowledge that was proposed in the papers [24,25] is adjusted to the description of data processing. The pragmatic system of knowledge representation is determined, as well as situations of semantic adequacy and semantic inadequacy for represented knowled…
Variable-Range Approximate Systems Induced by Many-Valued L-Relations
2014
The concept of a many-valued L-relation is introduced and studied. Many-valued L-relations are used to induce variable-range quasi-approximate systems defined on the lines of the paper (A. Sostak, Towards the theory of approximate systems: variable-range categories. Proceedings of ICTA2011, Cambridge Univ. Publ. (2012) 265–284.) Such variable-range (quasi-)approximate systems can be realized as special families of L-fuzzy rough sets indexed by elements of a complete lattice.
Generalized Rough Sets in Contextual Spaces
1997
This paper presents a generalization of Pawlak’s conception of rough sets [6] and [7]. It is more general than Pawlak’s solution of the problem of the definability of sets, the knowledge of which is incomplete and vague. The authors’ conception is based on conception of contextual space [4], which was inspired by Ziarko’s approach [12] to rough sets. Rough sets introduced by Pawlak [6] are particular cases of contextual rough sets defined in the contextual approximation space. This space is defined axiomatically by means of so called context relations. Every contextual rough set determined by set X can be determined by the union of the lower approximation of X and a subset of the boundary o…
Algebraic Structures of Rough Sets
1994
This paper deals with some algebraic and set-theoretical properties of rough sets. Our considerations are based on the original conception of rough sets formulated by Pawlak [4, 5]. Let U be any fixed non-empty set traditionally called the universe and let R be an equivalence relation on U. The pair A = (U, R) is called the approximation space. We will call the equivalence classes of the relation R the elementary sets. We denote the family of elementary sets by U/R. We assume that the empty set is also an elementary set. Every union of elementary sets will be called a composed set. We denote the family of composed sets by ComR. We can characterize each set X ⊆ U using the composed sets [5].