Proceedings ArticleDOI
Information quanta and approximation spaces II: generalised approximation spaces
P. Pagliani
- Vol. 2, pp 611-616
TLDR
The higher order notions of an " information quantum" an "information quantum relational system" which make adjoint operators into continuous approximation operators and make it possible to define a class of topological approximation spaces are introduced.Abstract:
In the first part we have introduced non-classical upper and lower approximations of subsets of objects or properties, on the basis of the properties featured by Galois adjunctions between intensional and extensionnal operators. In the present part we introduce the higher order notions of an "information quantum" an "information quantum relational system" which make adjoint operators into continuous approximation operators and make it possible to define a class of topological approximation spaces.read more
Citations
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Journal ArticleDOI
Topology vs generalized rough sets
Zhi Pei,Daowu Pei,Li Zheng +2 more
TL;DR: It is proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.
Journal ArticleDOI
Connections between covering-based rough sets and concept lattices
Anhui Tan,Jinjin Li,Guoping Lin +2 more
TL;DR: This study systematically explores their connections in terms of approximation operators, structures and knowledge reduction to conclude that the approximation spaces of coverings and concept lattices are related and that their reducts are coincident.
Proceedings ArticleDOI
Information quanta and approximation spaces. I. Non-classical approximation operators
TL;DR: In the first part of this paper property systems are investigated in order to define intensional and extensional operators fulfilling adjointness properties, and the higher order notion of an "information quantum" is introduced to bypass "discontinuity" of such operators.
Book ChapterDOI
Formal topology and information systems
TL;DR: Rough Set Theory may be considered as a formal interpretation of observation of phenomena by synthesizing relations between objects and properties into systems of relations betweenObjects and objects and objects.
Book ChapterDOI
Transforming information systems
TL;DR: This paper discusses how to transform Information Systems in order to apply a well-funded set of operators and to improve their precision.
References
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Book
A Compendium of Continuous Lattices
TL;DR: In this article, the authors present a primer of complete lattices and complete topology of continuous lattices, including the Scott topology and meet-continuous lattices.
Journal ArticleDOI
From Concept Lattices to Approximation Spaces: Algebraic Structures of Some Spaces of Partial Objects.
TL;DR: It is shown through some examples that many program derivation strategies described in the literature, such as the methodology for eliminating unnecessary variables, the tupling strategy, the partial deduction techniques, and the promotion strategy, can be viewed as particular instances of ow abstract strategy.
Book ChapterDOI
Information Systems, Similarity Relations and Modal Logics
TL;DR: The completeness theorems for the introduced modal logics with respect to their standard semantics are introduced and their “query meaning” is discussed.
Book ChapterDOI
Intuitionistic formal spaces and their neighbourhood
TL;DR: In this paper, the authors provide simple and complete propositional semantics for Girard's linear logic and for usual intuitionistic logic, by isolating and disregarding those conditions which correspond to the structural rules of weakening and contraction.
Journal ArticleDOI
Formal Topology and Domains
TL;DR: In this paper, the relation between formal topology and the theory of domains is discussed, and it is shown that some open problems in one of the two fields could already have a solution in the other, and that is why an intensification of contact should be rewarding.