Approximation of sets based on partial covering
type: Item
instance of: scholarly article
title: Approximation of sets based on partial covering
zbMATH Open document ID: 1230.68194
published in: Theoretical Computer Science
publication date: 2011-10-27T00:00:00Z
full work available at URL: http://hdl.handle.net/2437/128729
review text: The paper presents a generalization of the rough set theory. The starting point is an arbitrary nonempty family \(\mathfrak{B}\) of subsets of an arbitrary nonempty universe of discourse \(U\); its elements are called \(\mathfrak{B}\)-sets. In analogy to the definition of the \(\sigma\)-algebra \(\sigma(U/\varepsilon)\), \(\mathfrak{D}_{\mathfrak{B}}\) represents the extension of \(\mathfrak{B}\) with the empty set and all the unions of some \(\mathfrak{B}\)-sets. The notions of lower and upper approximations are straightforward point-free generalizations of Pawlak's same approximations imitating the \(\varepsilon\)-elementary set based formulations; both of them belong to \(\mathfrak{D}_{\mathfrak{B}}\). The entire discussion is within an overall approximation framework whose scope ranges from weak approximation pairs of maps on \(U\) to the notion of a Galois connection on \(2^U\). The common features of the rough set theory and the approach from this paper are treated uniformly, and most notions of Pawlak's rough set theory constitute compound ones and they are split into two or more parts; this framework helps to understand the state of their compound nature and to specify their constituents in a more general context. To demonstrate the effectiveness of the proposed approach a real life biological example is examined. It is based on the META program which is a grid-based, landscape-ecology-oriented, satellite-image supported, field vegetation mapping method of Hungarian habitats.
reviewed by: Ion Iancu
Mathematics Subject Classification ID: 68T37
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03E75
zbMATH DE Number: 5964202
zbMATH Keywords: rough set theory
zbMATH Keywords: vagueness
zbMATH Keywords: Galois connection
zbMATH Keywords: recognition and evaluation of natural vegetation heritage
author: Zoltán Csajbók
MaRDI profile type: Publication
OpenAlex ID: W2042273122
cites work: Rough sets
cites work: Q4003537
cites work: Rudiments of rough sets
cites work: Q4014403
cites work: Rough sets determined by quasiorders
cites work: Q4426928
cites work: Rough Set Approximations in Formal Concept Analysis
cites work: Q3429641
cites work: Topological approaches to covering rough sets
cites work: Information granulation and rough set approximation
cites work: Information granules: Towards foundations of granular computing
cites work: Transactions on Rough Sets III
cites work: Approximation Theories: Granular Computing vs Rough Sets
cites work: Q4825689
cites work: Approximate Boolean Reasoning: Foundations and Applications in Data Mining
cites work: Lattice Theory for Rough Sets
cites work: Two views of the theory of rough sets in finite universes
cites work: Constructive and algebraic methods of the theory of rough sets
cites work: Extensions and intensions in the rough set theory
cites work: Relationship between generalized rough sets based on binary relation and covering
cites work: Q4400871
cites work: Q3346320
cites work: Q4007176
cites work: Theory and Applications of Relational Structures as Knowledge Instruments
cites work: Q4316881
cites work: Q4530231
cites work: Q4828280
cites work: A geometry of approximation. Rough set theory: logic, algebra and topology of conceptual patterns.
cites work: Continuous Lattices and Domains
cites work: Q3425583
cites work: A unifying study between modal-like operators, topologies and fuzzy sets
DOI: 10.1016/J.TCS.2011.05.037
description: scientific article; zbMATH DE number 5964202