Algebraic properties and measures of uncertainty in rough set on two universal sets based on multi-granulation
22 Aug 2013-pp 24
TL;DR: Some algebraic properties and measures of uncertainty of multi-granulation rough set for two universal sets U and V are defined and studied to help in describing and solving real life problems more accurately.
Abstract: The fundamental concept of crisp set has been extended in many directions in recent past. The notion of rough set by Pawlak being noteworthy among them. A rough set captures indiscernibility of elements in a set. In the view of granular computing, rough set model is researched by single granulation. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define some algebraic properties and measures of uncertainty of multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.
Citations
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TL;DR: The basic concepts, operations and characteristics on the rough set theory are introduced, and then the extensions of rough set model, the situation of their applications, some application software and the key problems in applied research for the roughSet theory are presented.
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TL;DR: This paper identifies the conventionally used rough computing techniques and discusses their concepts, developments, abstraction, hybridization, and scope of applications.
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01 Jan 2014
TL;DR: This chapter defines multigranulation rough set for two universal sets U and V and the algebraic properties, measures of uncertainty and topological characterization that are interesting in the theory of multig Granular rough sets are studied.
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TL;DR: In this article , the authors proposed outlier detection in single universal sets using an intuitionistic fuzzy proximity relation with a rough set based on complement entropy and weighted density approach, and the empirical study has been considered for ranking the colleges based on the parameters evaluated.
Abstract: Data mining is a technique for analyzing larger datasets to identify patterns, information, and relationships that may be used to solve challenging problems. Identifying outliers has attracted the focus of researchers working on a variety of areas. Outliers are things that behave differently from other objects. With real-world data, rough set theory can cope with ambiguity and uncertainty. So far, the study has solely focused on spotting outliers using the membership function. Outliers may be recognized using membership and non-membership values, however, utilizing the principle of intuitionistic fuzzy proximity relation. At this step, the indiscernibility of objects is discovered, and the quantitative data is then converted to qualitative data. This article proposes outlier detection in single universal sets using an intuitionistic fuzzy proximity relation with a rough set based on complement entropy and weighted density approach. The empirical study has been considered for ranking the colleges based on the parameters evaluated.
References
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TL;DR: 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.
Abstract: 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.
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TL;DR: Methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis are discussed.
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TL;DR: This paper reviews and compares constructive and algebraic approaches in the study of rough set algebras and states axioms that must be satisfied by the operators.
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