Dealing with Missing Data: Algorithms Based on Fuzzy Set and Rough Set Theories

2005 ◽  
pp. 37-57 ◽  
Author(s):  
Dan Li ◽  
Jitender Deogun ◽  
William Spaulding ◽  
Bill Shuart
Keyword(s):  
Missing Data ◽  
Rough Set ◽  
Fuzzy Set

scholarly journals Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 949
Author(s):  
Zhen Li ◽  
Xiaoyan Zhang
Keyword(s):  
Information Theory ◽  
Pattern Recognition ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Fuzzy Set ◽  
Equivalence Relation ◽  
Target Concept ◽  
Actual Case ◽  
Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

Data Clustering Algorithms Using Rough Sets

2013 ◽  
pp. 297-327 ◽  
Author(s):  
B.K. Tripathy ◽  
Adhir Ghosh
Keyword(s):  
Comparative Study ◽  
Rough Set ◽  
Fuzzy Clustering ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Data Clustering ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Future Studies ◽  
Multiple Clusters

Developing Data Clustering algorithms have been pursued by researchers since the introduction of k-means algorithm (Macqueen 1967; Lloyd 1982). These algorithms were subsequently modified to handle categorical data. In order to handle the situations where objects can have memberships in multiple clusters, fuzzy clustering and rough clustering methods were introduced (Lingras et al 2003, 2004a). There are many extensions of these initial algorithms (Lingras et al 2004b; Lingras 2007; Mitra 2004; Peters 2006, 2007). The MMR algorithm (Parmar et al 2007), its extensions (Tripathy et al 2009, 2011a, 2011b) and the MADE algorithm (Herawan et al 2010) use rough set techniques for clustering. In this chapter, the authors focus on rough set based clustering algorithms and provide a comparative study of all the fuzzy set based and rough set based clustering algorithms in terms of their efficiency. They also present problems for future studies in the direction of the topics covered.

Data Discovery Approaches for Vague Spatial Data

Data Mining ◽  
2013 ◽  
pp. 50-65
Author(s):  
Frederick E. Petry
Keyword(s):  
Data Mining ◽  
Fuzzy Sets ◽  
Association Rules ◽  
Rough Set ◽  
Fuzzy Set ◽  
Spatial Data ◽  
Spatial Databases ◽  
Uncertain Data ◽  
Rule Extraction ◽  
Data Discovery

This chapter focuses on the application of the discovery of association rules in approaches vague spatial databases. The background of data mining and uncertainty representations using rough set and fuzzy set techniques is provided. The extensions of association rule extraction for uncertain data as represented by rough and fuzzy sets is described. Finally, an example of rule extraction for both types of uncertainty representations is given.

A Hybrid Scheme for Breast Cancer Detection Using Intuitionistic Fuzzy Rough Set Technique

Biometrics ◽  
2017 ◽  
pp. 1195-1219 ◽  
Author(s):  
Chiranji Lal Chowdhary ◽  
D. P. Acharjya
Keyword(s):  
Feature Extraction ◽  
Rough Set ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Hybrid Scheme ◽  
Fuzzy Rough Set ◽  
Intuitionistic Fuzzy ◽  
Prime Concern ◽  
Diagnosis Of Cancer ◽  
Occurrence Matrix

Diagnosis of cancer is of prime concern in recent years. Medical imaging is used to analyze these diseases. But, these images contain uncertainties due to various factors and thus intelligent techniques are essential to process these uncertainties. This paper hybridizes intuitionistic fuzzy set and rough set in combination with statistical feature extraction techniques. The hybrid scheme starts with image segmentation using intuitionistic fuzzy set to extract the zone of interest and then to enhance the edges surrounding it. Further feature extraction using gray-level co-occurrence matrix is presented. Additionally, rough set is used to engender all minimal reducts and rules. These rules then fed into a classifier to identify different zones of interest and to check whether these points contain decision class value as either cancer or not. The experimental analysis shows the overall accuracy of 98.3% and it is higher than the accuracy achieved by hybridizing fuzzy rough set model.

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.

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