Probabilistic Approaches to the Rough Set Theory and Their Applications in Decision-Making

Rough sets were presented by Professor Zdzislaw Pawlak in a seminal paper published in 1982. Rough Sets Theory (RST) has evolved into a methodology for dealing with different types of problems, such as the uncertainty produced by inconsistencies in data. RST is the best tool for modeling uncertainty when it shows up as inconsistency, according to several analyses. This is the main reason for which the RST has been included in the family of Soft Computing techniques. The classical RST is defined by using an equivalence relation as an indiscernibility relation. This is very restrictive in different domains, so several extensions of the theory have been formulated. One of these alternatives is based on a probabilistic approach, where several variants have been proposed such as the Variable Precision Rough Sets model, Rough Bayesian model, and Parameterized Rough Set model. Here is presented an analysis about the evolution of the RST in order to enrich the applicability to solve real problems by means of the probabilistic approaches of rough sets and its application to knowledge discovering and decision making, two main activities in Business Intelligence.

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