Proceedings ArticleDOI
Information quanta and approximation spaces. I. Non-classical approximation operators
P. Pagliani
- Vol. 2, pp 605-610
TLDR
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.Abstract:
In the first part of this paper property systems are investigated in order to define intensional and extensional operators fulfilling adjointness properties. On this basis a set of operators are defined which are able to determine non-classical upper and lower approximations of subsets of objects or properties. But in order to bypass "discontinuity" of such operators we introduce, in the second part, the higher order notion of an "information quantum". This way we can account for attribute systems as well as property systems by transforming them into new structures called "information quantum relational systems" in which adjointness makes operators fulfil continuity and makes it possible to define a class of generalised approximation spaces.read more
Citations
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Journal Article
Rough set approximations in formal concept analysis
Yiyu Yao,Yaohua Chen +1 more
TL;DR: The notion of rough set approximations is introduced into formal concept analysis and approximation operators are defined based on both lattice- theoretic and set-theoretic operators to provide a better understanding of data analysis.
Journal ArticleDOI
Formal reasoning with rough sets in multiple-source approximation systems
Md. Aquil Khan,Mohua Banerjee +1 more
TL;DR: To facilitate formal reasoning with rough sets in MSASs, a quantified propositional modal logic LMSAS is proposed and is shown to be sound and complete with respect to this semantics.
Proceedings ArticleDOI
Rough set approximations in formal concept analysis
Yiyu Yao,Yaohua Chen +1 more
TL;DR: In this paper, the notion of rough set approximations is introduced into formal concept analysis, and the approximation operators are defined based on both lattice-theoretic and set-theory operators.
Journal ArticleDOI
Rough set model based on formal concept analysis
TL;DR: A rough set model based on formal concept analysis is proposed and a complete and non-redundant set of decision dependencies can be obtained from a decision table, providing a better understanding of rough set theory from the perspective of formal conceptAnalysis.
Book ChapterDOI
Propositional logics from rough set theory
Mohua Banerjee,Md. Aquil Khan +1 more
TL;DR: An attempt is made to place the gamut of work on propositional logics with semantics based on rough sets, spread over the last 20 years, in one platform, and present the various relationships that emerge and indicate questions that surface.
References
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Book ChapterDOI
A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis
TL;DR: The theory of rough sets and formal concept analysis are compared in a common framework based on formal contexts to produce different types of rules summarizing knowledge embedded in data.
Book ChapterDOI
Power Domains and Predicate Transformers: A Topological View
TL;DR: The specific tasks are to provide a more adequate framework for power-domain constructions; and to show that the connection between (Dijkstra's) weakest preconditions and the Smyth powerdomain, established by Plotkin for the case of flat domains, actually holds in full generality.
Proceedings ArticleDOI
Modal-style operators in qualitative data analysis
N. Duntsch,G. Gediga +1 more
TL;DR: The usage of the modal possibility operator (and its dual necessity operator) in qualitative data analysis is explored, and it is shown that it-quite literally-complements the derivation operator of formal concept analysis.
Book ChapterDOI
Granular Computing using Neighborhood Systems
TL;DR: A set-theoretic framework is proposed for granular computing that examines the notions of rough sets and qualitative fuzzy sets and provides a basis for the proposed framework of granular Computing.
Book ChapterDOI
Granular Computing on Binary Relations Analysis of Conflict and Chinese Wall Security Policy
TL;DR: In this article, a study of the granular computing on binary relations is presented, which is applied to the analysis of conflict of interests relation (CIR) and the Chinese wall security policy (CWSP).