scholarly journals The “Logical Or” Rough Set Theory of Variable Precision and Grade Based on Dominance Relation in Intuitionistic Fuzzy Information System

2016 ◽  
Vol 06 (02) ◽  
pp. 66-77
Author(s):  
猛 胡
Keyword(s):  
Information System ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Dominance Relation ◽  
Fuzzy Information ◽  
Variable Precision ◽  
Intuitionistic Fuzzy

Degree Dominance Interval Relation-Based RSM in Intuitionistic Fuzzy Decision Systems

2011 ◽  
Vol 48-49 ◽  
pp. 357-361
Author(s):  
Bing Huang
Keyword(s):  
Knowledge Representation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Decision Rules ◽  
Dominance Relation ◽  
Fuzzy Decision ◽  
Decision Systems ◽  
Intuitionistic Fuzzy ◽  
Interval Relation

By introducing a degree dominance relation to dominance interval intuitionistic fuzzy decision systems, we establish a degree dominance interval rough set model (RSM), which is mainly based on replacing the indiscernibility relation in classical rough set theory with the degree dominance interval relation. To simplify knowledge representation and extract some nontrivial simpler degree dominance interval intuitionistic fuzzy decision rules, we propose two attribute reductions of the degree dominance interval intuitionistic fuzzy decision systems that eliminate the redundant condition attributes that are not essential from the viewpoint of degree dominance interval intuitionistic fuzzy decision rules.

Incremental Approach for Updating Approximations of Variable Precision Rough Set Based on Dominance Relations

2014 ◽  
Vol 631-632 ◽  
pp. 49-52
Author(s):  
Yan Li ◽  
Jia Jia Hou ◽  
Xiao Qing Liu
Keyword(s):  
Information System ◽  
Rough Set ◽  
Dominance Relation ◽  
Incremental Updating ◽  
Dominance Relations ◽  
Incremental Approach ◽  
Variable Precision ◽  
Variable Precision Rough Set ◽  
Over Time

Variable precision rough set (VPRS) based on dominance relation is an extension of traditional rough set by which can handle preference-ordered information flexibly. This paper focuses on the maintenance of approximations in dominance based VPRS when the objects in an information system vary over time. The incremental updating principles are given as inserting or deleting an object, and some experimental evaluations validates the effectiveness of the proposed method.

Rough set theory for the interval-valued fuzzy information systems

2008 ◽  
Vol 178 (8) ◽  
pp. 1968-1985 ◽  
Author(s):  
Zengtai Gong ◽  
Bingzhen Sun ◽  
Degang Chen
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Information ◽  
Interval Valued

On Quasi Discrete Topological Spaces in Information Systems

2012 ◽  
Vol 3 (2) ◽  
pp. 38-52 ◽  
Author(s):  
Tutut Herawan
Keyword(s):  
Information System ◽  
Information Systems ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Discrete Topology

This paper presents an alternative way for constructing a topological space in an information system. Rough set theory for reasoning about data in information systems is used to construct the topology. Using the concept of an indiscernibility relation in rough set theory, it is shown that the topology constructed is a quasi-discrete topology. Furthermore, the dependency of attributes is applied for defining finer topology and further characterizing the roughness property of a set. Meanwhile, the notions of base and sub-base of the topology are applied to find attributes reduction and degree of rough membership, respectively.

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.

THE ALGORITHM ON KNOWLEDGE REDUCTION IN INCOMPLETE INFORMATION SYSTEMS

2002 ◽  
Vol 10 (01) ◽  
pp. 95-103 ◽  
Author(s):  
JIYE LIANG ◽  
ZONGBEN XU
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Np Hard ◽  
Knowledge Reduction ◽  
Np Hard Problem ◽  
Incomplete Information Systems

Rough set theory is emerging as a powerful tool for reasoning about data, knowledge reduction is one of the important topics in the research on rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem of attributes. In this paper, knowledge reduction is defined from the view of information, a heuristic algorithm based on rough entropy for knowledge reduction is proposed in incomplete information systems, the time complexity of this algorithm is O(|A|2|U|). An illustrative example is provided that shows the application potential of the algorithm.

scholarly journals Using Variable Precision Rough Set for Selection and Classification of Biological Knowledge Integrated in DNA Gene Expression

2012 ◽  
Vol 9 (3) ◽  
pp. 1-17 ◽  
Author(s):  
D. Calvo-Dmgz ◽  
J. F. Gálvez ◽  
D. Glez-Peña ◽  
S. Gómez-Meire ◽  
F. Fdez-Riverola
Keyword(s):  
Gene Expression ◽  
Set Theory ◽  
Rough Set ◽  
Microarray Data ◽  
Rough Set Theory ◽  
Biological Knowledge ◽  
Variable Precision ◽  
Gene Sets ◽  
Proposed Model ◽  
Variable Precision Rough Set

Summary DNA microarrays have contributed to the exponential growth of genomic and experimental data in the last decade. This large amount of gene expression data has been used by researchers seeking diagnosis of diseases like cancer using machine learning methods. In turn, explicit biological knowledge about gene functions has also grown tremendously over the last decade. This work integrates explicit biological knowledge, provided as gene sets, into the classication process by means of Variable Precision Rough Set Theory (VPRS). The proposed model is able to highlight which part of the provided biological knowledge has been important for classification. This paper presents a novel model for microarray data classification which is able to incorporate prior biological knowledge in the form of gene sets. Based on this knowledge, we transform the input microarray data into supergenes, and then we apply rough set theory to select the most promising supergenes and to derive a set of easy interpretable classification rules. The proposed model is evaluated over three breast cancer microarrays datasets obtaining successful results compared to classical classification techniques. The experimental results shows that there are not significat differences between our model and classical techniques but it is able to provide a biological-interpretable explanation of how it classifies new samples.

Intuitionistic Fuzzy Neighborhood Rough Set Model for Feature Selection

2018 ◽  
Vol 7 (2) ◽  
pp. 75-84 ◽  
Author(s):  
Shivam Shreevastava ◽  
Anoop Kumar Tiwari ◽  
Tanmoy Som
Keyword(s):  
Feature Selection ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Continuous Data ◽  
Feature Subset ◽  
Data Set ◽  
Intuitionistic Fuzzy ◽  
Neighborhood Models ◽  
Neighborhood Rough Set

Feature selection is one of the widely used pre-processing techniques to deal with large data sets. In this context, rough set theory has been successfully implemented for feature selection of discrete data set but in case of continuous data set it requires discretization, which may cause information loss. Fuzzy rough set theory approaches have also been used successfully to resolve this issue as it can handle continuous data directly. Moreover, almost all feature selection techniques are used to handle homogeneous data set. In this article, the center of attraction is on heterogeneous feature subset reduction. A novel intuitionistic fuzzy neighborhood models have been proposed by combining intuitionistic fuzzy sets and neighborhood rough set models by taking an appropriate pair of lower and upper approximations and generalize it for feature selection, supported with theory and its validation. An appropriate algorithm along with application to a data set has been added.

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