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.

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.

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.

Uncertainty Measure Based on Evidence Theory

2013 ◽  
Vol 329 ◽  
pp. 344-348
Author(s):  
Shao Pu Zhang ◽  
Tao Feng
Keyword(s):  
Information System ◽  
Information Fusion ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Belief Function ◽  
Mass Function ◽  
Uncertainty Measure ◽  
Rough Approximation ◽  
Uncertainty Information ◽  
Uncertainty Method

Evidence theory is an effective method to deal with uncertainty information. And uncertainty measure is to reflect the uncertainty of an information system. Thus we want to merge evidence theory with uncertainty method in order to measure the roughness of a rough approximation space. This paper discusses the information fusion and uncertainty measure based on rough set theory. First, we propose a new method of information fusion based on the Bayse function, and define a pair of belief function and plausibility function using the fused mass function in an information system. Then we construct entropy for every decision class to measure the roughness of every decision class, and entropy for decision information system to measure the consistence of decision table.

Multigranulation roughness based on soft relations

2021 ◽  
pp. 1-16
Author(s):  
Muhammad Shabir ◽  
Jamalud Din ◽  
Irfan Ahmad Ganie
Keyword(s):  
Finite Number ◽  
Rough Set ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Soft Sets ◽  
Upper Approximation ◽  
Special Cases ◽  
Multigranulation Rough Set ◽  
Empty Subset ◽  
Lower And Upper Approximations

The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian et al, extended this model and defined multigranulation rough sets by using finite number of equivalence relations. This model provide new direction to the research. Recently, Shabir et al. proposed a rough set model which depends on a soft relation from an universe V to an universe W . In this paper we are present multigranulation roughness based on soft relations. Firstly we approximate a non-empty subset with respect to aftersets and foresets of finite number of soft binary relations. In this way we get two sets of soft sets called the lower approximation and upper approximation with respect to aftersets and with respect to foresets. Then we investigate some properties of lower and upper approximations of the new multigranulation rough set model. It can be found that the Pawlak rough set model, Qian et al. multigranulation rough set model, Shabir et al. rough set model are special cases of this new multigranulation rough set model. Finally, we added two examples to illustrate this multigranulation rough set model.

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.

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 A Novel Decision-Making Approach to Fund Investments Based on Multigranulation Rough Set

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Xima Yue ◽  
Xiang Su
Keyword(s):  
Decision Making ◽  
Information System ◽  
Rough Set ◽  
Investment Decision ◽  
Decision Rules ◽  
Investment Project ◽  
Point Of View ◽  
New Approach ◽  
Multigranulation Rough Set ◽  
Fund Investment

Fund investment is a hot issue in today’s society. How to choose a project for investment is affected by many factors. In view of this problem, this paper starts from the granular computing point of view and combines the multigranulation rough set decision-making method to construct a fund investment decision information system; then, the fund investment decision information system is reduced under different thresholds, and the decision rules are extracted through reduction. And from the aspects of decision accuracy and rule accuracy, the rules are analyzed. Finally, decision rules are used to give the decision of the fund investment project. This study provides a new approach to fund management.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

scholarly journals Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 949
Author(s):  
Zhen Li ◽  
Xiaoyan Zhang
Keyword(s):  
Information Theory ◽  
Pattern Recognition ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Fuzzy Set ◽  
Equivalence Relation ◽  
Target Concept ◽  
Actual Case ◽  
Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

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