GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

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.

Deep learning architecture using rough sets and rough neural networks

Kybernetes ◽  
2017 ◽  
Vol 46 (4) ◽  
pp. 693-705 ◽  
Author(s):  
Yasser F. Hassan
Keyword(s):  
Machine Learning ◽  
Deep Learning ◽  
Soft Computing ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Decision Table ◽  
Content Type ◽  
Real World Applications ◽  
Decision Tables

Purpose This paper aims to utilize machine learning and soft computing to propose a new method of rough sets using deep learning architecture for many real-world applications. Design/methodology/approach The objective of this work is to propose a model for deep rough set theory that uses more than decision table and approximating these tables to a classification system, i.e. the paper propose a novel framework of deep learning based on multi-decision tables. Findings The paper tries to coordinate the local properties of individual decision table to provide an appropriate global decision from the system. Research limitations/implications The rough set learning assumes the existence of a single decision table, whereas real-world decision problem implies several decisions with several different decision tables. The new proposed model can handle multi-decision tables. Practical implications The proposed classification model is implemented on social networks with preferred features which are freely distribute as social entities with accuracy around 91 per cent. Social implications The deep learning using rough sets theory simulate the way of brain thinking and can solve the problem of existence of different information about same problem in different decision systems Originality/value This paper utilizes machine learning and soft computing to propose a new method of rough sets using deep learning architecture for many real-world applications.

scholarly journals Feature Genes Selection Using Fuzzy Rough Uncertainty Metric for Tumor Diagnosis

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.

Generalized dynamic attribute reduction based on similarity relation of intuitionistic fuzzy rough set

2020 ◽  
Vol 39 (5) ◽  
pp. 7107-7122
Author(s):  
Zhang Chuanchao
Keyword(s):  
Big Data ◽  
Information Systems ◽  
Rough Set ◽  
Rough Sets ◽  
Attribute Reduction ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Data Set ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Rough Sets

In view of the characteristics with big data, high feature dimension, and dynamic for a large-scale intuitionistic fuzzy information systems, this paper integrates intuitionistic fuzzy rough sets and generalized dynamic sampling theory, proposes a generalized attribute reduction algorithm based on similarity relation of intuitionistic fuzzy rough sets and dynamic reduction. It uses dynamic reduction sampling theory to divide a big data set into small data sets and relative positive domain cardinality instead of dependency degree as decision-making condition, and obtains reduction attributes of big intuitionistic fuzzy decision information systems, and achieves the goal of extracting key features and fault diagnosis. The innovation of this paper is that it integrates generalized dynamic reduction and intuitionistic fuzzy rough set, and solves the problem of big data set which cannot be solved by intuitionistic fuzzy rough set. Taking an actual data as an example, the scientificity, rationality and effectiveness of the algorithm are verified from the aspects of stability, diagnostic accuracy, optimization ability and time complexity. Compared with similar algorithms, the advantages of the proposed algorithm for big data processing are confirmed.

scholarly journals Fuzzy Covering-Based Three-Way Clustering

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dandan Yang
Keyword(s):  
Nearest Neighbor ◽  
Structural Information ◽  
Boundary Region ◽  
Global Perspective ◽  
Semantic Interpretation ◽  
Entropy Theory ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
The Universe ◽  
Better Than

This paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. First of all, a valid fuzzy covering of the universe is constructed on the basis of an appropriate fuzzy similarity relation, which helps capture the structural information and the internal connections of the dataset from the global perspective. Due to the advantages of valid fuzzy covering, we explore the valid fuzzy covering instead of the raw dataset for RFCM algorithm-based three-way clustering. Subsequently, from the perspective of semantic interpretation of balancing the uncertainty changes in fuzzy sets, a method of partition thresholds acquisition combining linear and nonlinear fuzzy entropy theory is proposed. Furthermore, boundary regions in three-way clustering correspond to the abstaining decisions and generate uncertain rules. In order to improve the classification accuracy, the k-nearest neighbor (kNN) algorithm is utilized to reduce the objects in the boundary regions. The experimental results show that the performance of the proposed three-way clustering based on fuzzy covering and kNN-FRFCM algorithm is better than the compared algorithms in most cases.

scholarly journals On Some Types of Covering-Based ℐ , T -Fuzzy Rough Sets and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Mohammed Atef ◽  
José Carlos R. Alcantud ◽  
Hussain AlSalman ◽  
Abdu Gumaei
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Practical Application ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Numerical Example ◽  
Variable Precision

The notions of the fuzzy β -minimal and maximal descriptions were established by Yang et al. (Yang and Hu, 2016 and 2019). Recently, Zhang et al. (Zhang et al. 2019) presented the fuzzy covering via ℐ , T -fuzzy rough set model ( FC ℐ T FRS ), and Jiang et al. (Jiang et al., in 2019) introduced the covering through variable precision ℐ , T -fuzzy rough sets ( CVP ℐ T FRS ). To generalize these models in (Jiang et al., 2019 and Zhang et al. 2019), that is, to improve the lower approximation and reduce the upper approximation, the present paper constructs eight novel models of an FC ℐ T FRS based on fuzzy β -minimal (maximal) descriptions. Characterizations of these models are discussed. Further, eight types of CVP ℐ T FRS are introduced, and we investigate the related properties. Relationships among these models are also proposed. Finally, we illustrate the above study with a numerical example that also describes its practical application.

A Matrix Method for Calculation of the Approximations under the Asymmetric Similarity Relation Based Rough Sets

2011 ◽  
Vol 187 ◽  
pp. 251-256
Author(s):  
Lei Wang ◽  
Tian Rui Li ◽  
Jun Ye
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Matrix Representation ◽  
Point Of View ◽  
Similarity Relation ◽  
The Matrix ◽  
Lower And Upper Approximations ◽  
Incomplete Information Systems ◽  
Asymmetric Similarity

The essence of the rough set theory (RST) is to deal with the inconsistent problems by two definable subsets which are called the lower and upper approximations respectively. Asymmetric Similarity relation based Rough Sets (ASRS) model is one kind of extensions of the classical rough set model in incomplete information systems. In this paper, we propose a new matrix view of ASRS model and give the matrix representation of the lower and upper approximations of a concept under ASRS model. According to this matrix view, a new method is obtained for calculation of the lower and upper approximations under ASRS model. An example is given to illustrate processes of calculating the approximations of a concept based on the matrix point of view.

Approximate Data Querying in Fuzzy Relational Database

2002 ◽  
Vol 6 (1) ◽  
pp. 33-40
Author(s):  
Rolly Intan ◽  
◽  
Masao Mukaidono ◽  
Keyword(s):  
Relational Database ◽  
Similarity Relation ◽  
Imprecise Data ◽  
Fuzzy Information ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Data Querying ◽  
Fuzzy Query ◽  
Probability Relation ◽  
Query System

Fuzzy relational database was proposed for dealing with imprecise data or fuzzy information in a relational database. In order to provide a more realistic relation in representing similarity between two imprecise data, we need to weaken fuzzy similarity relation to be weak fuzzy similarity relation in which fuzzy conditional probability relation (FCPR, for short) is regarded as a concrete example of the weak fuzzy similarity relation. In this paper, application of approximate data querying is discussed induced by FCPR in the presence of the fuzzy relational database. Application of approximate data querying in order to provide fuzzy query relation is presented into two frameworks, namely dependent inputs and independent inputs. Finally, related to join operator, approximate join of two or more fuzzy query relations is given for the purpose of extending query system.

Near sets through fuzzy similarity relation

2014 ◽  
Vol 8 ◽  
pp. 2035-2040
Author(s):  
Rogi Jacob ◽  
Sunny Kuriakose A
Keyword(s):  
Similarity Relation ◽  
Near Sets ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation
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