A Kind of Fuzzy Set for Rough Fuzzy Sorting Method

2015 ◽  
Vol 740 ◽  
pp. 786-789
Author(s):  
Jia Tai Gang ◽  
Kun Liang ◽  
Ming Ming Niu ◽  
Xue Sheng Liu
Keyword(s):  
Partial Order ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Approximate Expression ◽  
Sorting Method ◽  
Whole Process ◽  
Order Structures

Fuzzy set sorting method is studied in this prepare. Firstly, a sorting method of Fuzzy number is proposed under the condition of rough fuzzy number. Use rough fuzzy number to approach fuzzy set by rough set and fuzzy set; it is an approximate expression of fuzzy set. Secondly, prove partial order structures above method and give an example for fuzzy set sorting method, showing the whole process for the sorting method. Lastly, summarize the sorting method that is convenient, concise and easy to apply. It is enrich and supplement for fuzzy sorting method.

Rule Extraction Based on Interval-Valued Rough Fuzzy Sets

2014 ◽  
Vol 665 ◽  
pp. 668-673
Author(s):  
Hua Ni Qin ◽  
Da Rong Luo
Keyword(s):  
Knowledge Discovery ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Fuzzy Information ◽  
Modified Model ◽  
Sorting Method ◽  
Rough Fuzzy Set ◽  
General Sorting ◽  
Interval Valued

A model of interval-valued rough fuzzy set combining interval-valued fuzzy set and rough set is investigated in this paper. Firstly, considering the deficiency of general sorting method between any interval-valued fuzzy numbers, an improved sorting method and a pair of new approximation operators about minimum and maximum are presented. Based on the improved operators, a model of interval-valued rough fuzzy set is established. At last, by using the modified model of interval-valued rough fuzzy set, a method of knowledge discovery in interval-valued fuzzy information systems is investigated.

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.

ANALYSIS OF FUZZY QUEUES BY USING PENTAGONAL FUZZY NUMBER

2021 ◽  
Vol 23 (04) ◽  
pp. 211-224
Author(s):  
Gurcharan Singh ◽  
◽  
Baljodh Singh ◽  
Neelam Kumari ◽  
◽  
...  
Keyword(s):  
Probability Theory ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Queuing Theory ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Linguistic Terms

This paper deals with the fact thatpentagonal fuzzy numbers are pre-owned and systematic outcomes are discussed in real-life situations. The fuzzy set supposition is combined with well-established classical queuing theory but the classical queuing theory is far away from real-life situations. In this approach, we can use both fuzzy and probability theory to make this work more realistic with the help of the α-cut technique. Symmetric pentagonal fuzzy numbers are used to elaborate on the situation of the queue in linguistic terms.

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.

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