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1
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A rough set-based knowledge discovery process

100%
Zhong N., Skowron A.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
603-619
EN
The knowledge discovery from real-life databases is a multi-phase process consisting of numerous steps, including attribute selection, discretization of real-valued attributes, and rule induction. In the paper, we discuss a rule discovery process that is based on rough set theory. The core of the process is a soft hybrid induction system called the Generalized Distribution Table and Rough Set System (GDT-RS) for discovering classification rules from databases with uncertain and incomplete data. The system is based on a combination of Generalization Distribution Table (GDT) and the Rough Set methodologies. In the preprocessing, two modules, i.e. Rough Sets with Heuristics (RSH) and Rough Sets with Boolean Reasoning (RSBR), are used for attribute selection and discretization of real-valued attributes, respectively. We use a slope-collapse database as an example showing how rules can be discovered from a large, real-life database.
2
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Mode set focused hybrid estimation

100%
Rienmüller T., Hofbaur M., Travé-Massuyès L., Bayoudh M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 1
131-144
EN
Estimating the state of a hybrid system means accounting for the mode of operation or failure and the current state of the continuously valued entities concurrently. Existing hybrid estimation schemes try to overcome the problem of an exponentially growing number of possible mode-sequence/continuous-state combinations by merging hypotheses and/or deducing likelihood measures to identify tractable sets of the most likely hypotheses. However, they still suffer from unnecessarily high computational costs as the number of possible modes increases. Hybrid diagnosis schemes, on the other hand, estimate the current mode of operation/failure only, thus leaving the continuous evolution of the system implicit. This paper proposes a novel scheme that uses a combination of both the approaches in order to define posterior transition probabilities between the specified modes of the hybrid system, hence focusing better on relevant hypotheses. In order to demonstrate the effectiveness of the proposed method, the algorithm is applied to a satellite attitude control system and compared with existing hybrid estimation/diagnosis schemes, such as the Interacting Multiple Model (IMM) algorithm, a purely parity based method (HyDiag), and an existing hybrid Mode Estimation (hME) algorithm.
3
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Local analysis of hybrid systems on polyhedral sets with state-dependent switching

100%
Leth J., Wisniewski R.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
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nr 2
341-355
EN
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
4
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A novel continuous model to approximate time Petri nets: modelling and analysis

100%
Gu T., Dong R.
International Journal of Applied Mathematics and Computer Science
|
2005
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tom 15
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nr 1
141-150
EN
In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented. sm
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