scholarly journals Some Improved Correlation Coefficients for q-Rung Orthopair Fuzzy Sets and Their Applications in Cluster Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Huma Bashir ◽  
Syed Inayatullah ◽  
Ahmed Alsanad ◽  
Rukhshanda Anjum ◽  
Mogeeb Mosleh ◽  
...  
Keyword(s):  
Cluster Analysis ◽  
Fuzzy Sets ◽  
Correlation Coefficients ◽  
Clustering Problem ◽  
Single Opinion ◽  
Clustering Problems ◽  
Degree Of Similarity

The structure of q-rung orthopair fuzzy sets (q-ROFSs) is a generalization of fuzzy sets (FSs), intuitionistic FSs (IFSs), and Pythagorean FSs (PFSs). The notion of q-ROFSs has the proficiency of coping with uncertainty without any restrictions. In addition, the structure of q-ROFSs can effectively cope with the situations involving dual opinions without any restrictions, instead of dealing with only single opinion or dual opinions under certain restrictions. In clustering problems, the correlation coefficients are worthwhile because they provide the degree of similarity or correlation between two elements or sets. The theme of this study is to formulate the correlation coefficients for q-ROFSs that are basically the generalization of correlation coefficients of IFSs and PFSs. Moreover, an application of these correlation coefficients to a clustering problem is proposed. Also, an analysis of the outcomes is carried out. Furthermore, a comparison is carried out among the correlation coefficients for q-ROFSs and the existing ones. Finally, the downsides of the existing works and benefits of the correlation coefficients for q-ROFSs are discussed.

scholarly journals Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

2021 ◽  
Author(s):  
Mingwei Lin ◽  
Chao Huang ◽  
Riqing Chen ◽  
Hamido Fujita ◽  
Xing Wang
Keyword(s):  
Cluster Analysis ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Correlation Coefficients ◽  
Disease Diagnosis ◽  
Decision Makers ◽  
Membership Degree ◽  
Pythagorean Fuzzy Sets ◽  
And Cluster Analysis ◽  
The Relationship

AbstractCompared to the intuitionistic fuzzy sets, the Pythagorean fuzzy sets (PFSs) can provide the decision makers with more freedom to express their evaluation information. There exist some research results on the correlation coefficient between PFSs, but sometimes they fail to deal with the problems of disease diagnosis and cluster analysis. To tackle the drawbacks of the existing correlation coefficients between PFSs, some novel directional correlation coefficients are put forward to compute the relationship between two PFSs by taking four parameters of the PFSs into consideration, which are the membership degree, non-membership degree, strength of commitment, and direction of commitment. Afterwards, two practical examples are given to show the application of the proposed directional correlation coefficient in the disease diagnosis, and the application of the proposed weighted directional correlation coefficient in the cluster analysis. Finally, they are compared with the previous correlation coefficients that have been developed for PFSs.

Using Cluster Analysis to Improve Marketing Experiments

1971 ◽  
Vol 8 (3) ◽  
pp. 340-347 ◽  
Author(s):  
George S. Day ◽  
Roger M. Heeler
Keyword(s):  
Cluster Analysis ◽  
Space Representation ◽  
Reduced Space ◽  
High Degree ◽  
Degree Of Similarity ◽  
Sensitive Experiment ◽  
Selection Of

When the selection of a sample of stores or cities requires a high degree of similarity among the test units in order to ensure a sensitive experiment, the sample may no longer represent the market. These conflicting requirements can be satisfied by choosing the sample from clusters displayed in a reduced space representation of the market.

scholarly journals Cross-Scale Precipitation Variability in a Semiarid Catchment Area on the Western Slopes of the Central Andes

2018 ◽  
Vol 57 (3) ◽  
pp. 675-694 ◽  
Author(s):  
Katja Trachte ◽  
Jochen Seidel ◽  
Rafael Figueroa ◽  
Marco Otto ◽  
Joerg Bendix
Keyword(s):  
Cluster Analysis ◽  
Catchment Area ◽  
Altitudinal Gradient ◽  
Large Scale ◽  
Wrf Model ◽  
Correlation Coefficients ◽  
Elevational Gradient ◽  
Central Andes ◽  
Precipitation Variability ◽  
Precipitation Regimes

AbstractSpatiotemporal precipitation patterns were investigated on the western slopes of the central Andes Mountains by applying EOF and cluster analysis as well as the Weather Research and Forecasting (WRF) Model. In the semiarid catchment area in the highlands of Lima, Peru, the precipitation is assumed to be a cross-scale interplay of large-scale dynamics, varying sea surface temperatures (SSTs), and breeze-dominated slope flows. The EOF analysis was used to encompass and elucidate the upper-level circulation patterns dominating the transport of moisture. To delineate local precipitation regimes, a partitioning cluster analysis was carried out, which additionally should illustrate local effects such as the altitudinal gradient of the Andes. The results demonstrated that especially during the transition to the dry season, synoptic-scale circulation aloft controls the precipitation (correlation coefficients between 0.6 and 0.9), whereas in the remaining seasons the slope breezes due to the altitudinal gradient mainly determine the precipitation behavior. Further analysis with regard to the spatiotemporal precipitation variability revealed an inversion of the precipitation distribution along the elevational gradient within the study area, mainly during February (29%) and March (35%), that showed correlations with coastal SST patterns ranging between 0.56 and 0.67. WRF simulations of the underlying mechanisms disclosed that the large-scale circulation influences the thermally induced upslope flows while the strength of southeastern low-level winds related to the coastal SSTs caused a blocking of easterlies in the middle troposphere through a reduced anticyclonic effect. This interplay enables the generation of precipitation in the usually drier environment at lower elevations, which leads to a decrease in rainfall with increasing elevation.

GEOMETRIC ALGORITHMS FOR THE CONSTRAINED 1-D K-MEANS CLUSTERING PROBLEMS AND IMRT APPLICATIONS

2009 ◽  
Vol 20 (02) ◽  
pp. 361-377
Author(s):  
DANNY Z. CHEN ◽  
MARK A. HEALY ◽  
CHAO WANG ◽  
BIN XU
Keyword(s):  
Radiation Therapy ◽  
Treatment Planning ◽  
Intensity Modulated Radiation Therapy ◽  
Geometric Algorithms ◽  
Maximum Difference ◽  
Continuous Version ◽  
Heuristic Approaches ◽  
Clustering Problem ◽  
Intensity Modulated ◽  
Clustering Problems

In this paper, we present efficient geometric algorithms for the discrete constrained 1-D K-means clustering problem and extend our solutions to the continuous version of the problem. One key clustering constraint we consider is that the maximum difference in each cluster cannot be larger than a given threshold. These constrained 1-D K-means clustering problems appear in various applications, especially in intensity-modulated radiation therapy (IMRT). Our algorithms improve the efficiency and accuracy of the heuristic approaches used in clinical IMRT treatment planning.

Cluster analysis using different correlation coefficients

2006 ◽  
Vol 49 (4) ◽  
pp. 715-727 ◽  
Author(s):  
Seong S. Chae ◽  
Chansoo Kim ◽  
Jong-Min Kim ◽  
William D. Warde
Keyword(s):  
Cluster Analysis ◽  
Correlation Coefficients

Clustering Algorithm for Vehicle’s Driving Data Feature based on Integrated Navigation

2021 ◽  
Vol 13 (4) ◽  
Author(s):  
Na Guo ◽  
Yiyi Zhu
Keyword(s):  
Clustering Algorithm ◽  
Principal Component ◽  
Kernel Principal Component Analysis ◽  
Integrated Navigation ◽  
Clustering Problem ◽  
Incremental Method ◽  
Feature Parameters ◽  
Vehicle Acceleration ◽  
Feature Based ◽  
Clustering Problems

The clustering result of K-means clustering algorithm is affected by the initial clustering center and the clustering result is not always global optimal. Therefore, the clustering analysis of vehicle’s driving data feature based on integrated navigation is carried out based on global K-means clustering algorithm. The vehicle mathematical model based on GPS/DR integrated navigation is constructed and the vehicle’s driving data based on GPS/DR integrated navigation, such as vehicle acceleration, are collected. After extracting the vehicle’s driving data features, the feature parameters of vehicle’s driving data are dimensionally reduced based on kernel principal component analysis to reduce the redundancy of feature parameters. The global K-means clustering algorithm converts clustering problem into a series of sub-cluster clustering problems. At the end of each iteration, an incremental method is used to select the next cluster of optimal initial centers. After determining the optimal clustering number, the feature clustering of vehicle’s driving data is completed. The experimental results show that the global K-means clustering algorithm has a clustering error of only 1.37% for vehicle’s driving data features and achieves high precision clustering for vehicle’s driving data features.

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