scholarly journals Relative relation matrix-based approaches for updating approximations in multigranulation rough sets

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2253-2272
Author(s):  
Zhanglin Xian ◽  
Jinkun Chen ◽  
Peiqiu Yu
Keyword(s):  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Original Method ◽  
Complex Data ◽  
Dynamic Information ◽  
Useful Knowledge ◽  
Multigranulation Rough Set ◽  
High Computational Complexity ◽  
Relation Matrix

Multigranulation rough set (MGRS) theory has attracted much attention. However, with the advent of big data era, the attribute values may often change dynamically, which leads to high computational complexity when handling large and complex data. How to effectively obtain useful knowledge from the dynamic information system becomes an important issue in MGRS. Motivated by this requirement, in this paper, we propose relative relation matrix approaches for computing approximations in MGRS and updating them dynamically. A simplified relative relation matrix is used to calculate approximations in MGRS, it is showed that the space and time complexities are no more than that of the original method. Furthermore, relative relation matrix-based approaches for updating approximations in MGRS while refining or coarsening attribute values are proposed. Several incremental algorithms for updating approximations in MGRS are designed. Finally, experiments are conducted to evaluate the efficiency and validity of the proposed methods.

Maintaining Dynamic Information Systems Using Incremental Dominance-Based Rough Set Approach

2014 ◽  
Vol 631-632 ◽  
pp. 53-56
Author(s):  
Yan Li ◽  
Xiao Qing Liu ◽  
Jia Jia Hou
Keyword(s):  
Decision Making ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Rough Sets ◽  
Dynamic Information ◽  
Knowledge Reduction ◽  
Incremental Approach

Dominance-based rough sets approach (DRSA) is an effective tool to deal with information with preference-ordered attribute domain. In practice, many information systems may evolve when attribute values are changed. Updating set approximations for these dynamic information systems is a necessary step for further knowledge reduction and decision making in DRSA. The purpose of this paper is to present an incremental approach when the information system alters dynamically with the change of condition attribute values. The updating rules are given with proofs, and the experimental evaluations on UCI data show that the incremental approach outperforms the original non-incremental one.

Rough Set on Two Universal Sets Based on Multigranulation

2014 ◽  
pp. 159-179 ◽  
Author(s):  
D. P. Acharjya ◽  
Mary A. Geetha
Keyword(s):  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Real Life ◽  
Equivalence Relations ◽  
Topological Characterization ◽  
Life Problems ◽  
Multigranulation Rough Set ◽  
Algebraic Properties ◽  
The Universe

The fundamental concept of crisp set has been extended in many directions in the recent past. The notion of rough set by Pawlak is noteworthy among them. The rough set philosophy is based on the concept that there is some information associated with each object of the universe. There is a need to classify objects of the universe based on the indiscernibility relation among them. In the view of granular computing, rough set model is researched by single granulation. It has been extended to multigranular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. However, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multigranulation rough set on single universal set to multigranulation rough set on two universal sets. This chapter defines multigranulation rough set for two universal sets U and V. In addition, the algebraic properties, measures of uncertainty and topological characterization that are interesting in the theory of multigranular rough sets are studied. This helps in describing and solving real life problems more accurately.

scholarly journals Two Different Views for Generalized Rough Sets with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2275
Author(s):  
Radwan Abu-Gdairi ◽  
Mostafa A. El-Gayar ◽  
Mostafa K. El-Bably ◽  
Kamel K. Fleifel
Keyword(s):  
Decision Making ◽  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Real Life ◽  
Binary Relations ◽  
Medical Field ◽  
Good Decision ◽  
Heart Attacks ◽  
Generalized Rough Sets

Rough set philosophy is a significant methodology in the knowledge discovery of databases. In the present paper, we suggest new sorts of rough set approximations using a multi-knowledge base; that is, a family of the finite number of general binary relations via different methods. The proposed methods depend basically on a new neighborhood (called basic-neighborhood). Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak’s rough sets and some of their extensions as confirming in the present paper. We prove that the accuracy of the suggested approximations is the best. Many comparisons between these approaches and the previous methods are introduced. The main goal of the suggested techniques was to study the multi-information systems in order to extend the application field of rough set models. Thus, two important real-life applications are discussed to illustrate the importance of these methods. We applied the introduced approximations in a set-valued ordered information system in order to be accurate tools for decision-making. To illustrate our methods, we applied them to find the key foods that are healthy in nutrition modeling, as well as in the medical field to make a good decision regarding the heart attacks problem.

scholarly journals Some New Covering-Based Multigranulation Fuzzy Rough Sets and Corresponding Application in Multicriteria Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Zaibin Chang ◽  
Lingling Mao
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Large Scale ◽  
Rough Set Theory ◽  
Multicriteria Decision Making ◽  
Matrix Representations ◽  
Fuzzy Rough Set ◽  
Multicriteria Decision ◽  
Multigranulation Rough Set

Multigranulation rough set theory is an important tool to deal with the problem of multicriteria information system. The notion of fuzzy β -neighborhood has been used to construct some covering-based multigranulation fuzzy rough set (CMFRS) models through multigranulation fuzzy measure. But the β -neighborhood has not been used in these models, which can be seen as the bridge of fuzzy covering-based rough sets and covering-based rough sets. In this paper, the new concept of multigranulation fuzzy neighborhood measure and some types of covering-based multigranulation fuzzy rough set (CMFRS) models based on it are proposed. They can be seen as the further combination of fuzzy sets: covering-based rough sets and multigranulation rough sets. Moreover, they are used to solve the problem of multicriteria decision making. Firstly, the definition of multigranulation fuzzy neighborhood measure is given based on the concept of β -neighborhood. Moreover, four types of CMFRS models are constructed, as well as their characteristics and relationships. Then, novel matrix representations of them are investigated, which can satisfy the need of knowledge discovery from large-scale covering information systems. The matrix representations can be more easily implemented than set representations by computers. Finally, we apply them to manage the problem of multicriteria group decision making (MCGDM) and compare them with other methods.

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.

Generalized neighborhood systems-based pessimistic rough sets and their applications in incomplete information systems

2021 ◽  
pp. 1-13
Author(s):  
Jing Pang ◽  
Bingxue Yao ◽  
Lingqiang Li
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Rough Sets ◽  
Decision Model ◽  
Incomplete Information System ◽  
Basic Properties ◽  
Model Based ◽  
Incomplete Information Systems

In this paper, we point out that Lin’s general neighborhood systems-based rough set model is an extension of Qian’s optimistic rough set model, and thus called optimistic general neighborhood systmes-based rough set model. Then we present a new rough set model based on general neighborhood systems, and prove that it is an extension of Qian’s pessimistic rough set model. Later, we study the basic properties of the proposed pessimistic rough sets, and define the serial, reflexive, symmetric, transitive and Euclidean conditions for general neighborhood systems, and explore the further properties of related rough sets. Furthermore, we apply the pessimistic general neighborhood systems-based rough set model in the research of incomplete information system, and build a three-way decision model based on it. A simple practical example to show the effectiveness of our model is also presented.

scholarly journals Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory

Information ◽  
2019 ◽  
Vol 10 (11) ◽  
pp. 334 ◽  
Author(s):  
Xiaoying You ◽  
Jinjin Li ◽  
Hongkun Wang
Keyword(s):  
Information System ◽  
Rough Set ◽  
Evidence Theory ◽  
Belief Function ◽  
Relative Reduction ◽  
Reduction Theory ◽  
Research Topics ◽  
Knowledge Reduction ◽  
Multigranulation Rough Set ◽  
Lower And Upper Approximations

Relative reduction of multiple neighborhood-covering with multigranulation rough set has been one of the hot research topics in knowledge reduction theory. In this paper, we explore the relative reduction of covering information system by combining the neighborhood-covering pessimistic multigranulation rough set with evidence theory. First, the lower and upper approximations of multigranulation rough set in neighborhood-covering information systems are introduced based on the concept of neighborhood of objects. Second, the belief and plausibility functions from evidence theory are employed to characterize the approximations of neighborhood-covering multigranulation rough set. Then the relative reduction of neighborhood-covering information system is investigated by using the belief and plausibility functions. Finally, an algorithm for computing a relative reduction of neighborhood-covering pessimistic multigranulation rough set is proposed according to the significance of coverings defined by the belief function, and its validity is examined by a practical example.

scholarly journals An Attribute Reduction Method using Neighborhood Entropy Measures in Neighborhood Rough Sets

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 155 ◽  
Author(s):  
Lin Sun ◽  
Xiaoyu Zhang ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Classification Performance ◽  
Data Sets ◽  
Complex Data ◽  
Decision Systems ◽  
Neighborhood Rough Sets

Attribute reduction as an important preprocessing step for data mining, and has become a hot research topic in rough set theory. Neighborhood rough set theory can overcome the shortcoming that classical rough set theory may lose some useful information in the process of discretization for continuous-valued data sets. In this paper, to improve the classification performance of complex data, a novel attribute reduction method using neighborhood entropy measures, combining algebra view with information view, in neighborhood rough sets is proposed, which has the ability of dealing with continuous data whilst maintaining the classification information of original attributes. First, to efficiently analyze the uncertainty of knowledge in neighborhood rough sets, by combining neighborhood approximate precision with neighborhood entropy, a new average neighborhood entropy, based on the strong complementarity between the algebra definition of attribute significance and the definition of information view, is presented. Then, a concept of decision neighborhood entropy is investigated for handling the uncertainty and noisiness of neighborhood decision systems, which integrates the credibility degree with the coverage degree of neighborhood decision systems to fully reflect the decision ability of attributes. Moreover, some of their properties are derived and the relationships among these measures are established, which helps to understand the essence of knowledge content and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is proposed to improve the classification performance of complex data sets. The experimental results under an instance and several public data sets demonstrate that the proposed method is very effective for selecting the most relevant attributes with great classification performance.

scholarly journals Rough Set Approach to Incomplete Multiscale Information System

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Xibei Yang ◽  
Yong Qi ◽  
Dongjun Yu ◽  
Hualong Yu ◽  
Xiaoning Song ◽  
...  
Keyword(s):  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Decision Rules ◽  
Structured Data ◽  
Representation System ◽  
New Knowledge ◽  
Real World Applications ◽  
Knowledge Representation System ◽  
Different Levels

Multiscale information system is a new knowledge representation system for expressing the knowledge with different levels of granulations. In this paper, by considering the unknown values, which can be seen everywhere in real world applications, the incomplete multiscale information system is firstly investigated. The descriptor technique is employed to construct rough sets at different scales for analyzing the hierarchically structured data. The problem of unravelling decision rules at different scales is also addressed. Finally, the reduct descriptors are formulated to simplify decision rules, which can be derived from different scales. Some numerical examples are employed to substantiate the conceptual arguments.

Sheaf Representation of an Information System

2019 ◽  
Vol 6 (2) ◽  
pp. 73-83
Author(s):  
Pyla Vamsi Sagar ◽  
M. Phani Krishna Kishore
Keyword(s):  
Information System ◽  
Information Retrieval ◽  
Present Article ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Science And Technology ◽  
Gold Mine ◽  
Sheaf Representation

Ever since Pawlak introduced the concepts of rough sets, it has attracted many researchers and scientists from various fields of science and technology. Particularly for algebraists as it presented a gold mine to explore the algebraic and topological connections with rough set theory. The present article deals with the connections between rough sets and sheaves. The authors studied sheaf representation of an information system in rough set framework and illustrated how it helps information retrieval.

Sign in / Sign up

Export Citation Format

Share Document