Research on approximation set of rough set based on fuzzy similarity

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

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A fuzzy similarity-based rough set approach for attribute selection in set-valued information systems

Soft Computing ◽

10.1007/s00500-019-04228-4 ◽

2019 ◽

Vol 24 (6) ◽

pp. 4675-4691 ◽

Cited By ~ 2

Author(s):

Shivani Singh ◽

Shivam Shreevastava ◽

Tanmoy Som ◽

Gaurav Somani

Keyword(s):

Information Systems ◽

Rough Set ◽

Attribute Selection ◽

Fuzzy Similarity

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Fuzzy Attribute Reduction Based on Fuzzy Similarity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.533.237 ◽

2014 ◽

Vol 533 ◽

pp. 237-241

Author(s):

Xiao Jing Liu ◽

Wei Feng Du ◽

Xiao Min

Keyword(s):

Set Theory ◽

Rough Set ◽

Equivalence Relation ◽

Rough Set Theory ◽

Attribute Reduction ◽

Decision Table ◽

Reduction Algorithm ◽

Fuzzy Decision ◽

Core Content ◽

Fuzzy Similarity

The measure of the significance of the attribute and attribute reduction is one of the core content of rough set theory. The classical rough set model based on equivalence relation, suitable for dealing with discrete-valued attributes. Fuzzy-rough set theory, integrating fuzzy set and rough set theory together, extending equivalence relation to fuzzy relation, can deal with fuzzy-valued attributes. By analyzing three problems of FRAR which is a fuzzy decision table attribute reduction algorithm having extensive use, this paper proposes a new reduction algorithm which has better overcome the problem, can handle larger fuzzy decision table. Experimental results show that our reduction algorithm is much quicker than the FRAR algorithm.

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Feature Genes Selection Using Fuzzy Rough Uncertainty Metric for Tumor Diagnosis

Computational and Mathematical Methods in Medicine ◽

10.1155/2019/6705648 ◽

2019 ◽

Vol 2019 ◽

pp. 1-9

Author(s):

Jiucheng Xu ◽

Yun Wang ◽

Keqiang Xu ◽

Tianli Zhang

Keyword(s):

Rough Set ◽

Conditional Entropy ◽

Similarity Relation ◽

Selection Algorithm ◽

Fuzzy Similarity ◽

Fuzzy Similarity Relation ◽

Definition Of ◽

Selection Of ◽

Original Information ◽

Metric Model

To select more effective feature genes, many existing algorithms focus on the selection and study of evaluation methods for feature genes, ignoring the accurate mapping of original information in data processing. Therefore, for solving this problem, a new model is proposed in this paper: rough uncertainty metric model. First, the fuzzy neighborhood granule of the sample is constructed by combining the fuzzy similarity relation with the neighborhood radius in the rough set, and the rough decision is defined by using the fuzzy similarity relation and the decision equivalence class. Then, the fuzzy neighborhood granule and the rough decision are introduced into the conditional entropy, and the rough uncertainty metric model is proposed; in the meantime, the definition of measuring the significance of feature genes and the proof of some related theorems are given. To make this model tolerate noises in data, this paper introduces a variable precision model and discusses the selection of parameters. Finally, based on the rough uncertainty metric model, we design a feature genes selection algorithm and compare it with some existing similar algorithms. The experimental results show that the proposed algorithm can select the smaller feature genes subset with higher classification accuracy and verify that the model proposed in this paper is more effective.

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IRIS Data Classification Using Tolerant Rough Sets1

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2000.p0327 ◽

2000 ◽

Vol 4 (5) ◽

pp. 327-335 ◽

Cited By ~ 6

Author(s):

Daijin Kim ◽

◽

Sung-Yang Bang

Keyword(s):

Similarity Measure ◽

Rough Set ◽

Data Classification ◽

Threshold Value ◽

Classification Method ◽

Data Set ◽

Upper Approximation ◽

Similarity Threshold ◽

Approximation Set ◽

Iris Data

This paper proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Similarity measure between two data points is described by a distance function of all constituent attributes and they are defined to be tolerant when their similarity measure exceeds a similarity threshold value. The determination of the optimal similarity threshold value is very important for accurate classification, so we determine it optimally by using the genetic algorithm (GA), where the goal of evolution is to balance two requirements so (1) some tolerant objects are required to be included in the same class as many as possible and (2) some objects in the same class are required to be tolerable as possible. After finding the optimal similarity threshold value, a tolerant set of each object is obtained and data set is grouped into the lower and upper approximation set depending on the coincidence of their classes. We propose a two-stage classification method where all data is classified by using the lower approximation at the first stage and then the nonclassified data at the first stage is classified again by using the rough membership functions obtained from the upper approximation set. The validity of the proposed classification method is tested by applying it IRIS data classification and its classification performance and processing time are compared to those of other classification methods such as BPNN, OFUNN, and FCM.

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