Incomplete Information System and Rough Set Theory

Models and Attribute Reductions

verfasst von: Xibei Yang, Jingyu Yang

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

"Incomplete Information System and Rough Set Theory: Models and Attribute Reductions" covers theoretical study of generalizations of rough set model in various incomplete information systems. It discusses not only the regular attributes but also the criteria in the incomplete information systems. Based on different types of rough set models, the book presents the practical approaches to compute several reducts in terms of these models. The book is intended for researchers and postgraduate students in machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, and granular computing.

Dr. Xibei Yang is a lecturer at the School of Computer Science and Engineering, Jiangsu University of Science and Technology, China; Jingyu Yang is a professor at the School of Computer Science, Nanjing University of Science and Technology, China.

Inhaltsverzeichnis

Frontmatter

Indiscernibility Relation Based Rough Sets

Frontmatter

Chapter 1. Indiscernibility Relation, Rough Sets and Information System

Abstract

Pawlak’s rough set model, was firstly constructed on the basis of an indiscernibility relation. Such an indiscernibility relation is an intersection of some equivalence relations in knowledge base and then it is also an equivalence relation. This chapter introduced the basic concepts of Pawlak’s rough set, Ziarko’s variable precision rough set and Qian’s multigranulation rough sets. These models were all proposed on the basis of indiscernibility relation. Variable precision rough set generalizes classical rough approximation by introducing a threshold β. Such β value represents a bound on the conditional probability of an equivalence class, which are classified into the target concept. Multigranulation rough set uses a family of the indiscernibility relation instead of a single one to construct rough approximation. In multigranulation rough set approach, the optimistic and pessimistic multigranulation rough sets are two basic models.

Xibei Yang, Jingyu Yang

Incomplete Information Systems and Rough Sets

Frontmatter

Chapter 2. Expansions of Rough Sets in Incomplete Information Systems

Abstract

Generally speaking, an incomplete information system indicates a system with unknown values. In this chapter, several expanded rough sets approaches to incomplete information system have been introduced. Firstly, by assuming that the unknown values can be compared with any values in the domains of the corresponding attributes, the tolerance relation, valued tolerance relation, maximal consistent block, descriptor can be used to construct rough approximations, respectively. Secondly, by assuming that the unknown values cannot be compared with any values in the domains of the corresponding attributes, the similarity relation, difference relation can be used to construct rough approximations, respectively. Finally, by considering the above two different semantic explanations of the unknown values, the characteristic relation can be used to construct rough approximation.

Xibei Yang, Jingyu Yang

Chapter 3. Neighborhood System and Rough Set in Incomplete Information System

Abstract

As the first model for Granular Computing, neighborhood system has been widely investigated. In this chapter, the neighborhood system approach is introduced into the incomplete information system. By employing the coverings induced by maximal consistent blocks and support sets of descriptors, two different neighborhood systems can be obtained, respectively. By using the knowledge engineering view in Granular Computing, a new knowledge operation is defined on the neighborhood system, which can help us obtain more knowledge through the known knowledge. Furthermore, by using neighborhood system based rough set model, we can obtain the same lower approximations and smaller upper approximations than the maximal consistent block and descriptor based rough sets.

Xibei Yang, Jingyu Yang

Dominance-based Rough Sets and Incomplete Information Systems

Frontmatter

Chapter 4. Dominance-based Rough Sets in “*” Incomplete Information System

Abstract

Dominance-based rough set approach is a very important expansion of Pawlak’s rough set approach since the former takes the preference-ordered domains of the attributes into account. In this chapter, the dominance-based rough set approach is introduced into the incomplete information system, in which all unknown values can be compared with any other values in the domains of the corresponding attributes. The “↑” and “↓” descriptors are employed to generate all certain rules from the incomplete information system. Moreover, the expanded dominance relation is also compared with the limited dominance relation, from which we can conclude that the limited dominance-based rough set approach is more suitable than the expanded dominance-based rough set approach when dealing with the incomplete information system.

Xibei Yang, Jingyu Yang

Chapter 5. Dominance-based Rough Sets in “?” Incomplete Information System

Abstract

In this chapter, the dominance-based rough set approach is introduced into the incomplete information system, in which the unknown values cannot be compared with any other values in the domains of the corresponding attributes. The similarity dominance-based rough sets are then constructed in crisp and fuzzy system, respectively. The similarity dominance relation is a generalization of the similarity relation and the dominance relation. It should also be noticed that different from several dominance relations, which have been presented in Chapter 4, similarity dominance relation has two different forms, one is the similarity increasing preference and the other is the similarity decreasing preference.

Xibei Yang, Jingyu Yang

Incomplete Information Systems and Multigranulation Rough Sets

Frontmatter

Chapter 6. Multigranulation Rough Sets in Incomplete Information System

Abstract

Since multigranulation rough set is an important expansion of Pawlak’s rough set and then it is an interesting issue to explore multigranulation rough set approach to incomplete information system. In this chapter, by considering two different semantic explanations of the unknown values, the tolerance relations, similarity relations are employed to construct multigranulation rough sets in incomplete information system, respectively. Following Qian’s multigranulation rough set theory, the optimistic and pessimistic cases are also considered in this chapter. The rough set models defined in this chapter provide a new direction for the investigation of rough set theory in incomplete information system.

Xibei Yang, Jingyu Yang

Backmatter

Titel: Incomplete Information System and Rough Set Theory
verfasst von: Xibei Yang
Jingyu Yang
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-25935-7
Print ISBN: 978-3-642-25934-0
DOI: https://doi.org/10.1007/978-3-642-25935-7