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14
A Rough Set Perspective on Data and Knowledge
, 1999
"... Rough set theory was proposed by Zdzisław Pawlak [24, 25] in the early 1980's. Since then we have witnessed a systematic, worldwide growth of interest in rough set theory and its applications. Rough set theory deals with the analysis of classificatory properties of data tables. Data repres ..."
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Rough set theory was proposed by Zdzisław Pawlak [24, 25] in the early 1980's. Since then we have witnessed a systematic, worldwide growth of interest in rough set theory and its applications. Rough set theory deals with the analysis of classificatory properties of data tables. Data represented in the tables can be acquired from measurements or from human experts; although in principle it must be discrete, there exist today methods that allow processing continuous values. The main goal of the rough set analysis is synthesis of approximations of concepts. The most important issues in the synthesis process are:  construction of relevant primitive concepts from which approximations of more complex concepts are assembled,  similarity (closeness) measures between concepts,  construction of operations producing compound concepts from the primitive ones. This presentation shows how several aspects of the above problems are solved by the classical rough set approach and ...
Rough sets in KDD, in
 Musen (Eds.), Proceedings of Conference on Intelligent Information Processing (IIP2000), Publishing House of Electronic Industry
, 2000
"... Abstract: In recent years we witness a rapid growth of interest in rough set theory and its applications, worldwide. The theory has been followed by the development of several software systems that implement rough set operations, in particular for solving knowledge discovery and data mining tasks. ..."
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Abstract: In recent years we witness a rapid growth of interest in rough set theory and its applications, worldwide. The theory has been followed by the development of several software systems that implement rough set operations, in particular for solving knowledge discovery and data mining tasks. Rough sets are applied in domains, such as, for instance, medicine, finance, telecommunication, vibration analysis, conflict resolution, intelligent agents, pattern recognition, control theory, signal analysis, process industry, marketing, etc. We introduce basic notions and discuss methodologies for analyzing data and surveys some applications. In particular we present applications of rough set methods for feature selection, feature extraction, discovery of patterns and their applications for decomposition of large data
Collapsing Hierarchies in Parallel Communicating Grammar Systems With Communication By Command
, 1996
"... We investigate here, mainly from the point of view of the hierarchies generated by different classes of systems, two variants of the parallel communicating grammar systems with communication by command: the multiple and, respectively, the single communication case. We show that the hierarchies for r ..."
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Cited by 1 (1 self)
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We investigate here, mainly from the point of view of the hierarchies generated by different classes of systems, two variants of the parallel communicating grammar systems with communication by command: the multiple and, respectively, the single communication case. We show that the hierarchies for regular and linear components collapse in the single communication case and the hierarchy for contextsensitive components collapses in both multiple and single communication cases. By a result in [3], it will follow from our result on systems with contextsensitive components that also the hierarchy for contextfree components collapses in both cases. Some open problems are also formulated.
On the degree complexity of special noncontextfree languages with respect to PC grammar systems
 New Mexico State University Las Cruces
"... When modeling natural languages, three languages are of special interest. In natural languages, there occur phenomena like multiple agreements, crossed agreements and replication. These aspects are represented by the three languages K1 = {a n b n c n  n ≥ 1}, K2 = {a n b m c n d m  m, n ≥ 1} and K ..."
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When modeling natural languages, three languages are of special interest. In natural languages, there occur phenomena like multiple agreements, crossed agreements and replication. These aspects are represented by the three languages K1 = {a n b n c n  n ≥ 1}, K2 = {a n b m c n d m  m, n ≥ 1} and K3 = {ww  w ∈ {a, b} +}, respectively. In the present paper, we give parallel communicating grammar systems (PC grammar systems) that generate the languages K1, K2 and K3 but use less or less powerful components than those systems published so far. This improves existing results. 1
Parallel Communicating Grammar Systems with Terminal Transmission
, 2000
"... We introduce a new variant of PC grammar systems, called PC grammar systems with terminal transmission, PCGSTT for short. We show that rightlinear centralized PCGSTT have nice formal language theoretic properties: they are closed under gsm mappings (in particular, under intersection with regular se ..."
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We introduce a new variant of PC grammar systems, called PC grammar systems with terminal transmission, PCGSTT for short. We show that rightlinear centralized PCGSTT have nice formal language theoretic properties: they are closed under gsm mappings (in particular, under intersection with regular sets and under and homomorphisms) and union; a slight variant is, in addition, closed under concatenation and star; their power lies between that of nparallel grammars introduced by Wood and that of matrix languages of index n, and their relation to equal matrix grammars of degree n is discussed. We show that membership for these language classes is complete for NL. In a second part of the paper, we discuss questions concerning grammatical inference of these systems. More precisely, we show that PCGSTT whose component grammars are terminal distinguishable rightlinear, a notion introduced by Radhakrishnan and Nagaraja in [29, 30], are identifiable in the limit if certain data comm...
Chapter 12 Rough Sets and Rough Logic: A KDD Perspective
"... Abstract Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world–wide growth of interest in rough sets and their applications. The main goal of rough set analysis is induction of approximations of con ..."
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Abstract Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world–wide growth of interest in rough sets and their applications. The main goal of rough set analysis is induction of approximations of concepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete. A fortiori, we have to describe concepts of interest (features, properties, relations etc.) not completely but by means of their reflections (i.e. approximations) in the chosen language. The most important issues in this induction process are: – construction of relevant primitive concepts from which approximations of more complex concepts are assembled, – measures of inclusion and similarity (closeness) on concepts, – construction of operations producing complex concepts from the primitive ones.
unknown title
"... Motivated by pattern grammars of Dassow et al [3] and cooperating distributed grammar systems by Csuhaj – Varju et al [5], we introduce a new grammar system, called cooperating distributed pattern grammar system CDPGS. In this system all the components considered are Pattern grammars. The resultant ..."
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Motivated by pattern grammars of Dassow et al [3] and cooperating distributed grammar systems by Csuhaj – Varju et al [5], we introduce a new grammar system, called cooperating distributed pattern grammar system CDPGS. In this system all the components considered are Pattern grammars. The resultant family of languages is compared with other families of languages and also we introduce a learning algorithm for cooperating distributed pattern grammar system.
PARALLEL COMMUNICATING GRAMMAR SYSTEMS Bringing PC Grammar Systems Closer to Hoare’s CSP’s 1
"... Abstract. We consider here Parallel Communicating (PC) grammar systems with features inspired from Hoare’s model of Communicating Sequential Processes (CSP). Specifically, we consider (1) nondeterministic queries (in two variants: using sets of query symbols, such that one symbol from each set has t ..."
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Abstract. We consider here Parallel Communicating (PC) grammar systems with features inspired from Hoare’s model of Communicating Sequential Processes (CSP). Specifically, we consider (1) nondeterministic queries (in two variants: using sets of query symbols, such that one symbol from each set has to be answered, and querying by nonterminals, such that the queried grammars are those having as axioms the specified symbol), (2) flags indicating the fact that a component of the system is ready to communicate, and (3) patterns of the communicated strings. The generative power of the obtained PC grammar systems is investigated, in comparison with the power of usual classes of PC grammar systems and with classes of grammars in the Chomsky hierarchy.
Investigations on Parallel Communicating Grammar Systems
"... Contents Acknowledgment 3 1 Introduction 4 1.1 Grammar systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Parallel communicating grammar systems . . . . . . . . . . . . . . . . . . 9 1.2.1 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2 D ..."
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Contents Acknowledgment 3 1 Introduction 4 1.1 Grammar systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Parallel communicating grammar systems . . . . . . . . . . . . . . . . . . 9 1.2.1 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2 Different ways of functioning and communication . . . . . . . . . . 11 1.2.3 Generative capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Preliminaries and definitions 15 2.1 Formal language preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Parallel communicating grammar systems . . . . . . . . . . . . . . . . . . 16 3 Synchronization, communication, and normal forms 21 3.1 Different modes of communication . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Results for systems with Chomsky grammars as components . . . .
Grammars Working on Layered Strings
"... We consider first an operation with strings and languages suggested by superposed windows on the computer screen (as well as by cryptographic systems of Richelieu type): we assume that the strings contain usual symbols as well as a transparent symbol. Superposing two strings (justified to left), we ..."
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We consider first an operation with strings and languages suggested by superposed windows on the computer screen (as well as by cryptographic systems of Richelieu type): we assume that the strings contain usual symbols as well as a transparent symbol. Superposing two strings (justified to left), we produce a new string consisting of the symbols visible from above. This operation is investigated as an abstract operation on strings, then it is used in building a variant of grammar systems with the component grammars working on the layers of an array of strings. Each grammar can rewrite only symbols in its layer which are visible from above. The language generated in this way consists of strings of the visible symbols, produced at the end of a derivation. The power of several variants of these generative mechanisms is investigated for the case of two layered strings. When a matrixlike control on the work of the component grammars is considered, then a characterization of recursively enumerable languages is obtained. Keywords: regulated rewriting, grammar systems, visual languages, Chomsky hierarchy TUCS Research Group