Hierarchical Granular Clustering: An Emergence of Information Granules of Higher Type and Higher Order

Pedrycz, Witold; Al‐Hmouz, Rami; Balamash, Abdullah Saeed; Morfeq, Ali

doi:10.1109/tfuzz.2015.2417896

Cited by 48 publications

(13 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although its usefulness, the developed clustering method still has several limitations which may serve as suggestions for further research: In many real‐world clustering problems, the data set may be large scale, whereas the proposed clustering method is not easy to be used to solve the clustering problems with large‐scale data sets due to high computational complexity. It would be interesting to develop Pythagorean fuzzy C‐mean clustering algorithms for meeting the requirement of dealing with large‐scale data sets in data mining. In some qualitative clustering problems, it is convenient for the evaluators to employ linguistic variable or its extensions to express qualitative evaluation values of objects with respect to criteria, but the developed clustering method fails to deal with these qualitative clustering problems. In the future, we will analyze how objects can be grouped into clusters when the data set in the qualitative clustering problems takes the forms of linguistic variables or/and hesitant fuzzy linguistic term sets, etc. Various types of relationships usually exist among criteria in the clustering process, whereas the developed clustering method under the hypothesis that all criteria are independent fails to deal with the clustering problems with criteria interactions.…”

Section: Discussionmentioning

confidence: 99%

“…In some qualitative clustering problems, it is convenient for the evaluators to employ linguistic variable or its extensions to express qualitative evaluation values of objects with respect to criteria, but the developed clustering method fails to deal with these qualitative clustering problems. In the future, we will analyze how objects can be grouped into clusters when the data set in the qualitative clustering problems takes the forms of linguistic variables or/and hesitant fuzzy linguistic term sets, etc.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Pythagorean Fuzzy Clustering Analysis: A Hierarchical Clustering Algorithm with the Ratio Index-Based Ranking Methods

Zhang

2017

Int. J. Intell. Syst.

View full text Add to dashboard Cite

The Pythagorean fuzzy set introduced by R. R. Yager in 2014 is a useful tool to model imprecise and ambiguous information appearing in decision and clustering problems. In this study, we present a general type of distance measure for Pythagorean fuzzy numbers (PFNs) and propose a novel ratio index‐based ranking method of PFNs. The novel ranking method of PFNs has more powerful ability to discriminate the magnitude of PFNs than the existing ranking methods for PFNs, which is further extended to compare the magnitude of interval‐valued Pythagorean fuzzy numbers (IVPFNs). The IVPFN is a new extension of PFN, which is parallel to interval‐valued intuitionistic fuzzy number. We introduce a general type of distance measure for IVPFNs. Afterwards, we study a kind of clustering problems in Pythagorean fuzzy environments in which the evaluation values are expressed by PFNs and/or IVPFNs and develop a novel Pythagorean fuzzy agglomerative hierarchical clustering approach. In the proposed clustering method, we define the concept of the dissimilarity degree between two clusters for each criterion and introduce the clustering procedure in the criteria level. To take all the criteria into account, we also introduce the overall clustering procedure, which is based on the overall dissimilarity degrees for a fixed aggregation operator such as the commonly used weighted arithmetic average operator or the ordered weighted averaging operator. In the overall clustering process, (1) we present a deviation degree‐based method to derive the weights of criteria and further obtain the overall clustering results if the weights of criteria are completely unknown; (2) we employ the ratio index‐based ranking method of IVPFNs to obtain the overall clustering results if the weights of criteria are given in advance and are expressed by IVPFNs. The salient feature of the proposed clustering method is that it not only can address the clustering problems in which the weights of criteria are not given precisely in advance but also can manage simultaneously the PFNs and IVPFNs data.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Pythagorean Fuzzy Clustering Analysis: A Hierarchical Clustering Algorithm with the Ratio Index-Based Ranking Methods

Zhang

2017

Int. J. Intell. Syst.

View full text Add to dashboard Cite

show abstract

“…3 (drawn by Peters and Weber 2016), we show an example of granulation of objects. Useful references in this field are, e.g., Pedrycz and Bagiela 2002;Sanchez et al 2014;Gacek and Pedrycz 2015;Pedrycz et al 2015b;Peters and Weber 2016;Lingras et al 2016;Dubois and Prade 2016. In addition to cluster analysis, other areas of the exploratory multivariate statistics can benefit from the use of granular computing tools, such as regression analysis, principal component analysis, and so on.…”

Section: Final Remarks and Future Perspectivesmentioning

confidence: 99%

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

D’Urso

2017

Granul. Comput.

View full text Add to dashboard Cite

“…In some literatures, this step to analyze the data distribution can be considered as the granulation of information [6][7][8]. The information granules are extracted by analyzing numerical data distribution and other source of experimental evidence.…”

Section: Fuzzy C-means Clustering and Conditional Fuzzy C-means Clustmentioning

confidence: 99%

Identification of Plastic Wastes by Using Fuzzy Radial Basis Function Neural Networks Classifier with Conditional Fuzzy C-Means Clustering

Roh¹,

Oh²

2016

Journal of Electrical Engineering and Technology

View full text Add to dashboard Cite

-The techniques to recycle and reuse plastics attract public attention. These public attraction and needs result in improving the recycling technique. However, the identification technique for black plastic wastes still have big problem that the spectrum extracted from near infrared radiation spectroscopy is not clear and is contaminated by noise. To overcome this problem, we apply Raman spectroscopy to extract a clear spectrum of plastic material. In addition, to improve the classification ability of fuzzy Radial Basis Function Neural Networks, we apply supervised learning based clustering method instead of unsupervised clustering method. The conditional fuzzy C-Means clustering method, which is a kind of supervised learning based clustering algorithms, is used to determine the location of radial basis functions. The conditional fuzzy C-Means clustering analyzes the data distribution over input space under the supervision of auxiliary information. The auxiliary information is defined by using k Nearest Neighbor approach.

show abstract

Hierarchical Granular Clustering: An Emergence of Information Granules of Higher Type and Higher Order

Cited by 48 publications

References 27 publications

Pythagorean Fuzzy Clustering Analysis: A Hierarchical Clustering Algorithm with the Ratio Index-Based Ranking Methods

Pythagorean Fuzzy Clustering Analysis: A Hierarchical Clustering Algorithm with the Ratio Index-Based Ranking Methods

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

Identification of Plastic Wastes by Using Fuzzy Radial Basis Function Neural Networks Classifier with Conditional Fuzzy C-Means Clustering

Contact Info

Product

Resources

About