Rough sets and intelligent data analysis

Abstract

Rough set based data analysis starts from a data table, called an information system. The information system contains data about objects of interest characterized in terms of some attributes. Often we distinguish in the information system condition and decision attributes. Such information system is called a decision table. The decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table. With every decision table a set of decision rules, called a decision algorithm can be associated. It is shown that every decision algorithm reveals some well-known probabilistic properties, in particular it satisfies the total probability theorem and the BayesÕ theorem. These properties give a new method of drawing conclusions from data, without referring to prior and posterior probabilities, inherently associated with Bayesian reasoning.

Discovering Novel Knowledge Using Granule Mining

“…B determines a binary relation I(B) on T . The family of all equivalence classes of I(B), that is denoted by T /B, are referred to B − granules [3]. The class in T /B induced by t is denoted by B(t).…”

“…Rough set theory describes decision rules by decision table, which compresses databases into granules and reveals the associations between granules [3,4]. The advantage of using decision rules is to reduce the two-steps of association mining into one process.…”

Inconsistent Decision System: Rough Set Data Mining Strategy to Extract Decision Algorithm of a Numerical Distance Relay - Tutorial

“…In contrast to crisp sets, a rough set has boundary line cases -events that cannot be certainly classified either as members of the set or of its complement. Rough set theory is an alternative intelligent data analysis tool that can be employed to handle vagueness and inconsistencies [8].…”

Handling Numerical Missing Values Via Rough Sets

“…[10,11,12] a set is a collection of any objects, which according to some law can be considered as a whole. A lot of existing industrial and research data sets contain missing values.…”