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We introduce the bipolar complemented de Morgan Brouwer-Zadeh distributive lattice in order to give an algebraic model the to Dominance-based Rough Set Approach. We present also the concept of bipolar approximation space and we show how it can be induced from a bipolar quasi Brouwer-Zadeh lattice.
The paper investigates relationships between chemical structure, surface active properties and antibacterial activity of 70 bis-quaternary imidazolium chlorides. Chemical structure and properties of imidazolium chlorides were described by 7 condition attributes and antimicrobial properties were mapped by a decision attribute. Dominance-based Rough Set Approach (DRSA) was applied to discover a priori unknown rules exhibiting monotonicity relationships in the data, which hold in some parts of the evaluation space. Strong decision rules discovered in this way may enable creating prognostic models of new compounds with favorable antimicrobial properties. Moreover, relevance of the attributes estimated from the discovered rules allows to distinguish which of the structure and surface active properties describe compounds that have the most preferable and the least preferable antimicrobial properties.
In order to handle inconsistencies in ordinal and monotonic information systems, several relaxed versions of the Dominance-based Rough Set Approach (DRSA) have been proposed, e.g., VC-DRSA. These versions use special consistency measures to admit some inconsistent objects in the lower approximations. The minimal consistency level that has to be attained by objects included in the lower approximations is defined using a prior knowledge or a trial-and-error procedure. In order to avoid dependence on prior knowledge, an alternative way of handling inconsistencies is to iteratively eliminate the most inconsistent objects (according to some measure) until the information system becomes consistent. This idea is a base of a new method of handling inconsistencies presented in this paper and called TIPStoC. The TIPStoC algorithm is illustrated by an example from the area of telecommunication and the efficiency of the new method is proved by a computational experiment.
The aim of the article is to establish a list of capabilities with reference to children’s well being in Poland. This issue can be considered as a multicriterial classification problem where decision attributes classes are ordered due to the preference – criteria. We used a Dominance-based Rough Set Approach (DRSA) adapted to deal with missing values. Analysis was performed on data set collected in Zachodniopomorskie district as a result of survey conduction.
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