In this article, we discuss methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis.
Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition. The rough set concept overlaps-to some extent-with many other mathematical tools developed to deal with vagueness and uncertainty, in particular with the Dempster-Shafer theory of evidence [15]. The main difference is that the Dempster-Shafer theory uses belief functions as a main tool, while rough set theory makes use of sets-lower and upper approximations. Another relationship exists between fuzzy set theory and rough set theory [13]. Rough set theory does not compete with fuzzy set theory, with which it is frequently contrasted, but rather complements it [1]. In any case, rough set theory and fuzzy set theory are independent approaches to imperfect knowledge. Furthermore, some relationship exists between rough set theory and discriminant analysis [7], Boolean reasoning methods [16], and decision analysis [14]. One of the main advantages of rough set theory is that it does not need any preliminary or additional information about data, such as probability distribution in statistics, basic probability assignment in the Dempster-Shafer theory, or grade of membership or the value of possibility in fuzzy set theory [2]. AI emerging technologies
Abstract. The rough set concept is a new mathematical approach to imprecision, vagueness and uncertainty. To some extend it overlaps with fuzzy set theory and evidence theory -nevertheless the rough set theory can be viewed in its own rights, as an independent discipline. Many real-life applications of the theory have proved its practical usefulness. The paper presents the basic assumptions underlying the rough sets philosophy, gives its fundamental concepts and discusses briefly some areas of applications, in particular in decision support. Finally further problems are shortly outlined.
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.
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