scholarly journals Rough Multisets and Information Multisystems

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
K. P. Girish ◽  
Sunil Jacob John
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Lower And Upper Approximations ◽  
Types Of Information

Rough set theory uses the concept of upper and lower approximations to encapsulate inherent inconsistency in real-world objects. Information multisystems are represented using multisets instead of crisp sets. This paper begins with an overview of recent works on multisets and rough sets. Rough multiset is introduced in terms of lower and upper approximations and explores related properties. The paper concludes with an example of certain types of information multisystems.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

scholarly journals On rough sets, their recent extensions and applications

2010 ◽  
Vol 25 (4) ◽  
pp. 365-395 ◽  
Author(s):  
N. Mac Parthaláin ◽  
Q. Shen
Keyword(s):  
Data Mining ◽  
Pattern Recognition ◽  
Set Theory ◽  
Rough Set ◽  
Intelligent Control ◽  
Real World ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Enormous Amount ◽  
Real World Problems

AbstractRough set theory (RST) has enjoyed an enormous amount of attention in recent years and has been applied to many real-world problems including data mining, pattern recognition, and intelligent control. Much research has recently been carried out in respect of both the development of the underlying theory and the application to new problem domains. This paper attempts to summarize the advances in RST, its extensions, and their applications. It also identifies important areas which require further investigation. Typical example application domains are examined which demonstrate the success of the application of RST to a wide variety of areas and disciplines, and which also exhibit the strengths and limitations of the respective underlying approaches.

scholarly journals Bi-covering rough sets

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2361-2369
Author(s):  
Mohamed Abo-Elhamayel
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Inclusion Relation ◽  
Different Types ◽  
Paper Construct ◽  
Lower And Upper Approximations ◽  
The Universe

Rough set theory is a useful tool for knowledge discovery and data mining. Covering-based rough sets are important generalizations of the classical rough sets. Recently, the concept of the neighborhood has been applied to define different types of covering rough sets. In this paper, based on the notion of bi-neighborhood, four types of bi-neighborhoods related bi-covering rough sets were defined with their properties being discussed. We first show some basic properties of the introduced bi-neighborhoods. We then explore the relationships between the considered bi-covering rough sets and investigate the properties of them. Also, we show that new notions may be viewed as a generalization of the previous studies covering rough sets. Finally, figures are presented to show that the collection of all lower and upper approximations (bi-neighborhoods of all elements in the universe) introduced in this paper construct a lattice in terms of the inclusion relation ?.

Multi-Granular Computing through Rough Sets

2014 ◽  
pp. 1-34 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Intelligent Systems ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Point Of View ◽  
Information Granules ◽  
Computing Platform

Granular Computing has emerged as a framework in which information granules are represented and manipulated by intelligent systems. Granular Computing forms a unified conceptual and computing platform. Rough set theory put forth by Pawlak is based upon single equivalence relation taken at a time. Therefore, from a granular computing point of view, it is single granular computing. In 2006, Qiang et al. introduced a multi-granular computing using rough set, which was called optimistic multigranular rough sets after the introduction of another type of multigranular computing using rough sets called pessimistic multigranular rough sets being introduced by them in 2010. Since then, several properties of multigranulations have been studied. In addition, these basic notions on multigranular rough sets have been introduced. Some of these, called the Neighborhood-Based Multigranular Rough Sets (NMGRS) and the Covering-Based Multigranular Rough Sets (CBMGRS), have been added recently. In this chapter, the authors discuss all these topics on multigranular computing and suggest some problems for further study.

Information Veins and Resampling with Rough Set Theory

2011 ◽  
pp. 1034-1040
Author(s):  
Benjamin Griffiths
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Decision Rules ◽  
International Conference ◽  
Fuzzy Environment ◽  
Leave One Out ◽  
Variable Precision Rough Sets

Rough Set Theory (RST), since its introduction in Pawlak (1982), continues to develop as an effective tool in data mining. Within a set theoretical structure, its remit is closely concerned with the classification of objects to decision attribute values, based on their description by a number of condition attributes. With regards to RST, this classification is through the construction of ‘if .. then ..’ decision rules. The development of RST has been in many directions, amongst the earliest was with the allowance for miss-classification in the constructed decision rules, namely the Variable Precision Rough Sets model (VPRS) (Ziarko, 1993), the recent references for this include; Beynon (2001), Mi et al. (2004), and Slezak and Ziarko (2005). Further developments of RST have included; its operation within a fuzzy environment (Greco et al., 2006), and using a dominance relation based approach (Greco et al., 2004). The regular major international conferences of ‘International Conference on Rough Sets and Current Trends in Computing’ (RSCTC, 2004) and ‘International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing’ (RSFDGrC, 2005) continue to include RST research covering the varying directions of its development. This is true also for the associated book series entitled ‘Transactions on Rough Sets’ (Peters and Skowron, 2005), which further includes doctoral theses on this subject. What is true, is that RST is still evolving, with the eclectic attitude to its development meaning that the definitive concomitant RST data mining techniques are still to be realised. Grzymala-Busse and Ziarko (2000), in a defence of RST, discussed a number of points relevant to data mining, and also made comparisons between RST and other techniques. Within the area of data mining and the desire to identify relationships between condition attributes, the effectiveness of RST is particularly pertinent due to the inherent intent within RST type methodologies for data reduction and feature selection (Jensen and Shen, 2005). That is, subsets of condition attributes identified that perform the same role as all the condition attributes in a considered data set (termed ß-reducts in VPRS, see later). Chen (2001) addresses this, when discussing the original RST, they state it follows a reductionist approach and is lenient to inconsistent data (contradicting condition attributes - one aspect of underlying uncertainty). This encyclopaedia article describes and demonstrates the practical application of a RST type methodology in data mining, namely VPRS, using nascent software initially described in Griffiths and Beynon (2005). The use of VPRS, through its relative simplistic structure, outlines many of the rudiments of RST based methodologies. The software utilised is oriented towards ‘hands on’ data mining, with graphs presented that clearly elucidate ‘veins’ of possible information identified from ß-reducts, over different allowed levels of missclassification associated with the constructed decision rules (Beynon and Griffiths, 2004). Further findings are briefly reported when undertaking VPRS in a resampling environment, with leave-one-out and bootstrapping approaches adopted (Wisnowski et al., 2003). The importance of these results is in the identification of the more influential condition attributes, pertinent to accruing the most effective data mining results.

Rough Set Theory

2011 ◽  
pp. 783-789
Author(s):  
Malcolm J. Beynon
Keyword(s):  
Decision Support ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Customer Relationship ◽  
Classification Problems ◽  
Variable Precision ◽  
Variable Precision Rough Sets

Rough set theory (RST), since its introduction in Pawlak (1982), continues to develop as an effective tool in classification problems and decision support. In the majority of applications using RST based methodologies, there is the construction of ‘if .. then ..’ decision rules that are used to describe the results from an analysis. The variation of applications in management and decision making, using RST, recently includes discovering the operating rules of a Sicilian irrigation purpose reservoir (Barbagallo, Consoli, Pappalardo, Greco, & Zimbone, 2006), feature selection in customer relationship management (Tseng & Huang, 2007) and decisions that insurance companies make to satisfy customers’ needs (Shyng, Wang, Tzeng, & Wu, 2007). As a nascent symbolic machine learning technique, the popularity of RST is a direct consequence of its set theoretical operational processes, mitigating inhibiting issues associated with traditional techniques, such as within-group probability distribution assumptions (Beynon & Peel, 2001). Instead, the rudiments of the original RST are based on an indiscernibility relation, whereby objects are grouped into certain equivalence classes and inference taken from these groups. Characteristics like this mean that decision support will be built upon the underlying RST philosophy of “Let the data speak for itself” (Dunstch & Gediga, 1997). Recently, RST was viewed as being of fundamental importance in artificial intelligence and cognitive sciences, including decision analysis and decision support systems (Tseng & Huang, 2007). One of the first developments on RST was through the variable precision rough sets model (VPRSß), which allows a level of mis-classification to exist in the classification of objects, resulting in probabilistic rules (see Ziarko, 1993; Beynon, 2001; Li and Wang, 2004). VPRSß has specifically been applied as a potential decision support system with the UK Monopolies and Mergers Commission (Beynon & Driffield, 2005), predicting bank credit ratings (Griffiths & Beynon, 2005) and diffusion of medicaid home care programs (Kitchener, Beynon, & Harrington, 2004). Further developments of RST include extended variable precision rough sets (VPRSl,u), which infers asymmetric bounds on the possible classification and mis-classification of objects (Katzberg & Ziarko, 1996), dominance-based rough sets, which bases their approach around a dominance relation (Greco, Matarazzo, & Slowinski, 2004), fuzzy rough sets, which allows the grade of membership of objects to constructed sets (Greco, Inuiguchi, & Slowinski, 2006), and probabilistic bayesian rough sets model that considers an appropriate certainty gain function (Ziarko, 2005). A literal presentation of the diversity of work on RST can be viewed in the annual volumes of the Transactions on Rough Sets (most recent year 2006), also the annual conferences dedicated to RST and its developments (see for example, RSCTC, 2004). In this article, the theory underlying VPRSl,u is described, with its special case of VPRSß used in an example analysis. The utilisation of VPRSl,u, and VPRSß, is without loss of generality to other developments such as those referenced, its relative simplicity allows the non-proficient reader the opportunity to fully follow the details presented.

Rough Sets

2011 ◽  
pp. 129-151
Author(s):  
Theresa Beaubouef ◽  
Frederick E Petry
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Uncertainty Management ◽  
Database Model ◽  
Management Of Uncertainty ◽  
Object Oriented Database

This chapter discusses ways in which rough set theory can enhance databases by allowing for the management of uncertainty. Rough sets can be integrated into an underlying database model, relational or object oriented, and also used in design and querying of databases. Because rough sets are a versatile theory, they can also be combined with other theories. The authors discuss the rough relational database model, the rough object oriented database model, and fuzzy set and intuitionistic set extensions to each of these models. Comparisons and benefits of the various approaches are discussed, illustrating the usefulness and versatility of rough sets for uncertainty management in databases.

Rough Sets

2009 ◽  
pp. 1127-1150
Author(s):  
Theresa Beaubouef ◽  
Frederick E. Petry
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Relational Databases ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Uncertainty Management ◽  
Database Model ◽  
Management Of Uncertainty ◽  
Object Oriented Database

This chapter discusses ways in which rough-set theory can enhance databases by allowing for the management of uncertainty. Rough sets can be integrated into an underlying database model, relational or object oriented, and also used in the design and uerying of databases, because roughsets are a versatile theory, theories. The authors discuss the rough relational databases model, the rough object-oriented database model, and fuzzy set and intuitionistic set extensions to each of these models. Comparisons and benefits of the various approaches are discussed, illustrating the usefulness and versatility of rough sets for uncertainty management in databases.

scholarly journals Reduction of Neighborhood-Based Generalized Rough Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Zhaohao Wang ◽  
Lan Shu ◽  
Xiuyong Ding
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Open Problems ◽  
The Third ◽  
Generalized Rough Sets

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

scholarly journals Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 432 ◽  
Author(s):  
Vilém Novák
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Type Theory ◽  
Rough Set Theory ◽  
Basic Concepts ◽  
Alternative Set

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.

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