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Rough set theory is an extension of set theory which proposed by Pawlak (1991) for describe and classify the incomplete or insufficient information. Besides it is mathematical tool that overcome the uncertainties and doubts. Also it verifies logic, and allows inconsistent data and no certainty to the discovery of incomplete implications. It is made as incomplete, inadequate and vague information by organizing. Rough set organizes the suitable data for analysis.
In real-world applications may includes the some uncertain and incomplete attributes in the knowledge representation systems in dynamic situation, for this reason knowledge discovery and processing is very important for decision system. Meanwhile it is supported as a framework for conceptualizing and analyzing certain and uncertain types of data that is a powerful tool for discovering patterns with upper and lower approximations. Some of the studies used the rough set theory with minimum vertex cover problem (Chen et al.2015; Chen et al.2016); interval-valued information systems (Leung et al. 2008); intuitionistic fuzzy sets (Zhang et al. 2016; Huang et al, 2016) for knowledge discovery in feature selection (Huang et al. 2016) and rule induction (Lin et al. 2015). Shu & Qian (2015) and Yao & Zhao (2008) used the rough set theory for attribute reduction in pre-processing of the data mining and knowledge discovery. Macia-Perez et al. (2015) proposed the formal expansion of the rough set theory based algorithm for detection of the abnormal behaviour in outlier.
Key Terms in this Chapter
Cuckoo Search Algorithm: A method of global optimization based on the behaviour of cuckoos was proposed by Yang & Deb (2009) . The breeding behaviour types are, laid their eggs in the host nests; if not detected and destroyed, the eggs are hatched to chicks by the hosts.
Sensitivity analysis: Analysis of the uncertainty output in system is evaluated by the different certain or uncertain input.
Information System: It consists of objects and attributes that shown in table with rows-objects and columns-attributes.
Decision Support System: It is computer based information system that support decision making activities with inputs, user knowledge and expertise, outputs and decision components.
Attribute: Refers with decision table in rough set which is divided into two disjoint groups called condition and decision attributes (action, results, outcome, etc.).
Rough Set Theory: It is first described by Zdzislaw I. Pawlak in early 1980’s. Every object of the universe of discourse some information (data, knowledge) is associated with lower and upper approximation.
Incomplete Information: Three types of incomplete data consists of attribute values which are lost values; attribute missing values; irrelevant concept data in attribute.
Decision Rules: It determines decision with rules under certain and uncertain conditions.
Indiscernibility Relation: It is a central concept of Rough Set Theory which relates between two or more objects identical relation in subset of the attributes.
Alternative Set Theory: It means system set theory that related the positive set theory and constructive set theory.
Rough Relations: Collection of such relations is closed under different binary compositions such as, algebraic sum, algebraic product etc. for uncertainty and incomplete data.