scholarly journals Fuzzy Knowledge Distance with Three-Layer Perspectives in Neighborhood System

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jie Yang ◽  
Tian Luo ◽  
Fan Zhao ◽  
Shuai Li ◽  
Wei Zhou
Keyword(s):  
Rough Sets ◽  
Structural Information ◽  
Boundary Region ◽  
Basic Element ◽  
Target Concept ◽  
Information Granule ◽  
Density Peaks ◽  
Neighborhood System ◽  
Neighborhood Rough Sets ◽  
The Difference

Information granule is the basic element in granular computing (GrC), and it can be obtained according to the granulation criterion. In neighborhood rough sets, current uncertainty measures focus on computing the knowledge granulation of single granular space and have two main limitations: (i) neglecting the structural information of boundary regions and (ii) the inability to reflect the difference between neighborhood granular spaces with the same uncertainty for approximating a target concept. Firstly, a fuzziness-based uncertainty measure for neighborhood rough sets is introduced to characterize the structural information of boundary regions. Moreover, from the perspective of distance, based on the idea of density peaks, we present a fuzzy-neighborhood-granule-distance- (FNGD-) based method to discover the relationship between granules in a granular space. Then, to characterize the difference between granular spaces for approximating a target concept, we present the fuzzy neighborhood granular space distance (FNGSD) and fuzzy neighborhood boundary region distance (FNBRD). FNGD, FNGSD, and FNBRD are hierarchically organized from fineness to coarseness according to the semantics of granularity, which provide three-layer perspectives in the neighborhood system.

The cost-sensitive approximation of neighborhood rough sets and granular layer selection

2021 ◽  
pp. 1-11
Author(s):  
Jie Yang ◽  
Tian Luo ◽  
Lijuan Zeng ◽  
Xin Jin
Keyword(s):  
Rough Sets ◽  
Granular Layer ◽  
User Requirements ◽  
Extended Model ◽  
Target Concept ◽  
Approximation Model ◽  
Neighborhood Rough Sets ◽  
The Cost ◽  
Monotonically Decrease

Neighborhood rough sets (NRS) are the extended model of the classical rough sets. The NRS describe the target concept by upper and lower neighborhood approximation boundaries. However, the method of approximately describing the uncertain target concept with existed neighborhood information granules is not given. To solve this problem, the cost-sensitive approximation model of the NRS is proposed in this paper, and its related properties are analyzed. To obtain the optimal approximation granular layer, the cost-sensitive progressive mechanism is proposed by considering user requirements. The case study shows that the reasonable granular layer and its approximation can be obtained under certain constraints, which is suitable for cost-sensitive application scenarios. The experimental results show that the advantage of the proposed approximation model, moreover, the decision cost of the NRS approximation model will monotonically decrease with granularity being finer.

Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system

2012 ◽  
Vol 207 ◽  
pp. 66-78 ◽  
Author(s):  
Lijuan Wang ◽  
Xibei Yang ◽  
Jingyu Yang ◽  
Chen Wu
Keyword(s):  
Rough Sets ◽  
Neighborhood System ◽  
Generalized Rough Sets

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.

Periodically poled KTA crystal investigated using coherent X-ray beams

2000 ◽  
Vol 33 (4) ◽  
pp. 1149-1153 ◽  
Author(s):  
P. Pernot-Rejmánková ◽  
P. A. Thomas ◽  
P. Cloetens ◽  
F. Lorut ◽  
J. Baruchel ◽  
...  
Keyword(s):  
Phase Difference ◽  
Domain Walls ◽  
Structural Information ◽  
Periodically Poled ◽  
Synchrotron Source ◽  
X Ray ◽  
Diffracted Waves ◽  
Coherent Beams ◽  
Diffraction Imaging ◽  
The Difference

The distribution of inverted ferroelectric domains on the surface and within the bulk of a periodically poled KTA (KTiOAsO4) single crystal has been observed using a simple X-ray diffraction imaging setup which takes advantage of the highly coherent beams available at a third-generation synchrotron source, such as the ESRF. This technique allows one to reveal the phase difference between the waves that are Bragg diffracted from adjacent domainsviafree-space propagation (Fresnel diffraction). The phase difference of the diffracted waves is mainly produced by the difference in phases of the structure factors involved, and contains precise structural information about the nature of the domain walls.

Subset neighborhood rough sets

2021 ◽  
pp. 107868
Author(s):  
Tareq M. Al-shami ◽  
Davide Ciucci
Keyword(s):  
Rough Sets ◽  
Neighborhood Rough Sets

MD-SPKM: A set pair k-modes clustering algorithm for incomplete categorical matrix data

2021 ◽  
Vol 25 (6) ◽  
pp. 1507-1524
Author(s):  
Chunying Zhang ◽  
Ruiyan Gao ◽  
Jiahao Wang ◽  
Song Chen ◽  
Fengchun Liu ◽  
...  
Keyword(s):  
Measurement Method ◽  
Clustering Algorithm ◽  
Average Distance ◽  
Boundary Region ◽  
Data Sets ◽  
Calculation Formula ◽  
Information Granule ◽  
Clustering Problem ◽  
Definition Of ◽  
Multiple Clusters

In order to solve the clustering problem with incomplete and categorical matrix data sets, and considering the uncertain relationship between samples and clusters, a set pair k-modes clustering algorithm is proposed (MD-SPKM). Firstly, the correlation theory of set pair information granule is introduced into k-modes clustering. By improving the distance formula of traditional k-modes algorithm, a set pair distance measurement method between incomplete matrix samples is defined. Secondly, considering the uncertain relationship between the sample and the cluster, the definition of the intra-cluster average distance and the threshold calculation formula to determine whether the sample belongs to multiple clusters is given, and then the result of set pair clustering is formed, which includes positive region, boundary region and negative region. Finally, through the selected three data sets and four contrast algorithms for experimental evaluation, the experimental results show that the set pair k-modes clustering algorithm can effectively handle incomplete categorical matrix data sets, and has good clustering performance in Accuracy, Recall, ARI and NMI.

scholarly journals A Neighborhood Rough Sets-Based Attribute Reduction Method Using Lebesgue and Entropy Measures

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 138 ◽  
Author(s):  
Lin Sun ◽  
Lanying Wang ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Rough Sets ◽  
Reduction Method ◽  
Attribute Reduction ◽  
Numerical Data ◽  
Classification Performance ◽  
Data Sets ◽  
Decision Systems ◽  
Public Data ◽  
Entropy Measures ◽  
Neighborhood Rough Sets

For continuous numerical data sets, neighborhood rough sets-based attribute reduction is an important step for improving classification performance. However, most of the traditional reduction algorithms can only handle finite sets, and yield low accuracy and high cardinality. In this paper, a novel attribute reduction method using Lebesgue and entropy measures in neighborhood rough sets is proposed, which has the ability of dealing with continuous numerical data whilst maintaining the original classification information. First, Fisher score method is employed to eliminate irrelevant attributes to significantly reduce computation complexity for high-dimensional data sets. Then, Lebesgue measure is introduced into neighborhood rough sets to investigate uncertainty measure. In order to analyze the uncertainty and noisy of neighborhood decision systems well, based on Lebesgue and entropy measures, some neighborhood entropy-based uncertainty measures are presented, and by combining algebra view with information view in neighborhood rough sets, a neighborhood roughness joint entropy is developed in neighborhood decision systems. Moreover, some of their properties are derived and the relationships are established, which help to understand the essence of knowledge and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is designed to improve the classification performance of large-scale complex data. The experimental results under an instance and several public data sets show that the proposed method is very effective for selecting the most relevant attributes with high classification accuracy.

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