Rough set models of interval rough number information system

2021 ◽  
Vol 40 (1) ◽  
pp. 1655-1666
Author(s):  
Linhai Cheng ◽  
Yu Zhang ◽  
Yingying He ◽  
Yuejin Lv
Keyword(s):  
Information System ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Uncertain Information ◽  
Approximation Accuracy ◽  
Similarity Degree ◽  
Application Range ◽  
Similar Relation ◽  
Degree Of Certainty

Classical rough set theory (RST) is based on equivalence relations, and does not have an effective mechanism when the attribute value of the objects is uncertain information. However, the information in actual problems is often uncertain, and an accurate or too vague description of the information can no longer fully meet the actual needs. Interval rough number (IRN) can reflect a certain degree of certainty in the uncertainty of the data when describing the uncertainty of the data, and can enable decision makers to make decisions more in line with actual needs according to their risk preferences. However, the current research on rough set models (RSMs) whose attribute values are interval rough numbers is still very scarce, and they cannot analyze the interval rough number information system (IRNIS) from the perspective of similar relation. therefore, three new interval rough number rough set models (IRNRSMs) based on similar relation are proposed in this paper. Firstly, aiming at the limitations of the existing interval similarity degree (ISD), new interval similarity degree and interval rough number similarity degree (IRNSD) are proposed, and their properties are discussed. Secondly, in the IRNIS, based on the newly proposed IRNSD, three IRNRSMs based on similar class, β-maximal consistent class and β-equivalent class are proposed, and their properties are discussed. And then, the relationships between these three IRNRSMs and those between their corresponding approximation accuracies are researched. Finally, it can be found that the IRNRSM based on the β-equivalent classes has the highest approximation accuracy. Proposing new IRNRSMs based on similar relation is a meaningful contribution to extending the application range of RST.

scholarly journals Rough Set Extension under Incomplete Information System with “?” Values

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Ahmed Hamed Hussein
Keyword(s):  
Information System ◽  
Incomplete Information ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Extended Model ◽  
Approximation Accuracy ◽  
Incomplete Information System ◽  
Similarity Class ◽  
Indiscernible Objects

Classical rough set theory (RST) can't process incomplete information system (IIS) because it is based on an indiscernibility relation which is a kind of equivalent relation. In the literature a non-symmetric similarity relation based rough set model (NS-RSM) has been introduced as an extended model under IIS with ``?" values directly. Unfortunately, in this model objects in the same similarity class are not necessarily similar to each other and may belong to different target classes. In this paper, a new inequivalent relation called Maximal Limited Consistent block relation (MLC) is proposed. The proposed MLC relation improves the lower approximation accuracy by finding the maximal limited blocks of indiscernible objects in IIS with ``?" values. Maximal Limited Similarity rough set model (MLS) is introduced as an integration between our proposed relation (MLC) and NS-RSM. The resulted MLS model works efficiently under IIS with ``?" values. Finally, an illustrative example is given to validate MLS model. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS. The results of this work demonstrate that the MLS model outperform NS-RSM.

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.

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 Fuzzy Set-Valued Information Systems and the Algorithm of Filling Missing Values for Incomplete Information Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Zhaohao Wang ◽  
Xiaoping Zhang
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Fuzzy Set ◽  
Missing Values ◽  
Rough Set Theory ◽  
Similarity Measures ◽  
New Information ◽  
Incomplete Information Systems

How to effectively deal with missing values in incomplete information systems (IISs) according to the research target is still a key issue for investigating IISs. If the missing values in IISs are not handled properly, they will destroy the internal connection of data and reduce the efficiency of data usage. In this paper, in order to establish effective methods for filling missing values, we propose a new information system, namely, a fuzzy set-valued information system (FSvIS). By means of the similarity measures of fuzzy sets, we obtain several binary relations in FSvISs, and we investigate the relationship among them. This is a foundation for the researches on FSvISs in terms of rough set approach. Then, we provide an algorithm to fill the missing values in IISs with fuzzy set values. In fact, this algorithm can transform an IIS into an FSvIS. Furthermore, we also construct an algorithm to fill the missing values in IISs with set values (or real values). The effectiveness of these algorithms is analyzed. The results showed that the proposed algorithms achieve higher correct rate than traditional algorithms, and they have good stability. Finally, we discuss the importance of these algorithms for investigating IISs from the viewpoint of rough set theory.

scholarly journals Using Rough Set to Construct the Enterprise Information Management System

2012 ◽  
Vol 6-7 ◽  
pp. 641-646
Author(s):  
Xing Wei
Keyword(s):  
Information Management ◽  
Set Theory ◽  
Rough Set ◽  
Management System ◽  
Rough Set Theory ◽  
Information Management System ◽  
Equivalence Relations ◽  
Knowledge Representation And Reasoning ◽  
Enterprise Information ◽  
Cpu Time

Rough set theory as a new hotspot in the field of artificial intelligence, it can effectively deal with incomplete and uncertain knowledge representation and reasoning. Rough set theory is built on the basis of the classification mechanism, it will be classified understand in a particular space on the equivalence relation, equivalence relations constitute the division of space. The paper puts forward using rough set to construct the enterprise information management system. The experiment shows the CPU Time in the attribute numbers, indicating that Jelonek is superior to rough set in building enterprise information management system.

Using Rough Set to Develop the Building Materials Management System

2013 ◽  
Vol 281 ◽  
pp. 658-663
Author(s):  
Jian Xu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Management System ◽  
Building Materials ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Materials Management ◽  
Cpu Time ◽  
Materials Used

Materials used in buildings are collectively referred to building materials. Building materials can be divided into structural materials, decoration materials and some special materials. Rough set theory is built on the basis of the classification mechanism, it will be classified understand in a particular space on the equivalence relation, equivalence relations constitute the division of space. The paper puts forward using rough set to develop the building materials management system. The experiment shows the CPU Time in the attribute numbers, indicating that rough set is superior to FCA in building materials management system.

A FPGA-Based Discretization Algorithm of Continuous Attributes in Rough Set

2013 ◽  
Vol 278-280 ◽  
pp. 1167-1173
Author(s):  
Guo Qiang Sun ◽  
Hong Li Wang ◽  
Jing Hui Lu ◽  
Xing He
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Processing Speed ◽  
Field Programmable Gate Array ◽  
Rough Set Theory ◽  
Continuous Data ◽  
Uncertain Information ◽  
Discretization Algorithm ◽  
Field Programmable ◽  
Speed Advantage

Rough set theory is mainly used for analysing, processing fuzzy and uncertain information and knowledge, but most of data that we usually gain are continuous data, rough set theory can pretreat these data and can gain satisfied discretization results. So, discretization of continuous attributes is an important part of rough set theory. Field Programmable Gate Array(FPGA) has been became the mainly platforms that realized design of digital system. In order to improve processing speed of discretization, this paper proposed a FPGA-based discretization algorithm of continuous attributes in rough ret that make use of the speed advantage of FPGA and combined attributes dependency degree. This method could save much time of pretreatment in rough ret and improve operation efficiency.

scholarly journals Evolving Lattices for Analyzing Behavioral Dynamics of Characters in Literary Text

2011 ◽  
Vol 9 (2) ◽  
pp. 502-509
Author(s):  
Eugene S Kitamura ◽  
Yukio-Pegio Gunji
Keyword(s):  
Rough Set ◽  
Text Analysis ◽  
Rough Set Theory ◽  
Window Size ◽  
Literary Text ◽  
Equivalence Relations ◽  
Behavior Dynamics ◽  
Behavioral Dynamics ◽  
The Relationship ◽  
Double Approximation

This paper is about an application of rough set derived lattices in order to analyze the dynamics of literary text. Due to the double approximation nature of rough set theory, a pseudo-closure obtained from two different equivalence relations allows us to form arbitrary lattices. Moreover, such double approximations with different equivalence relations permit us to obtain lattice fixed points based on two interpretations. The two interpretations used for literary text analysis are subjects and their attributes. The attributes chosen for this application are verbs. The progression of a story is defined by the sequence of verbs (or event occurrences). By fixing a window size and sliding the window down the story steps, we obtain a lattice representing the relationship between subjects and their attributes within that window frame. The resulting lattice provides information such as complementarity (lattice complement existence rate) and distributivity (lattice complement possession rate). These measurements depend on the overlap and the lack of overlap among the attributes of characters. As the story develops and new character and attributes are provided as the source of lattices, one can observe its evolution. In fact, a dramatic change in the behavior dynamics in a scene is reflected in the particular shifts in the character-attribute relationship. This method lets us quantify the developments of character behavioral dynamics in a story.

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6175-6183
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Properties ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation

2014 ◽  
Vol 1 (2) ◽  
pp. 49-61 ◽  
Author(s):  
Mary A. Geetha ◽  
D. P. Acharjya ◽  
N. Ch. S. N. Iyengar
Keyword(s):  
Information System ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Granular Computing ◽  
Real Life ◽  
Equivalence Relations ◽  
Life Problems ◽  
Algebraic Properties ◽  
The Universe

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.

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