Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set...Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.展开更多
Hierarchical clustering analysis based on statistic s is one of the most important mining algorithms, but the traditionary hierarchica l clustering method is based on global comparing, which only takes in Q clusteri n...Hierarchical clustering analysis based on statistic s is one of the most important mining algorithms, but the traditionary hierarchica l clustering method is based on global comparing, which only takes in Q clusteri ng while ignoring R clustering in practice, so it has some limitation especially when the number of sample and index is very large. Furthermore, because of igno ring the association between the different indexes, the clustering result is not good & true. In this paper, we present the model and the algorithm of two-level hierarchi cal clustering which integrates Q clustering with R clustering. Moreover, becaus e two-level hierarchical clustering is based on the respective clustering resul t of each class, the classification of the indexes directly effects on the a ccuracy of the final clustering result, how to appropriately classify the inde xes is the chief and difficult problem we must handle in advance. Although some literatures also have referred to the issue of the classificati on of the indexes, but the articles classify the indexes only according to their superficial signification, which is unscientific. The reasons are as follow s: First, the superficial signification of some indexes usually takes on different meanings and it is easy to be misapprehended by different person. Furthermore, t his classification method seldom make use of history data, the classification re sult is not so objective. Second, for some indexes, its superficial signification didn’t show any mean ings, so simply from the superficial signification, we can’t classify them to c ertain classes. Third, this classification method need the users have higher level knowledge of this field, otherwise it is difficult for the users to understand the signifi cation of some indexes, which sometimes is not available. So in this paper, to this question, we first use R clustering method to cluste ring indexes, dividing p dimension indexes into q classes, then adopt two-level clustering method to get the final result. Obviously, the classification result is more objective and accurate. Moreover, after the first step, we can get the relation of the different indexes and their interaction. We can also know under a certain class indexes, which samples can be clustering to a class. (These semi finished results sometimes are very useful.) The experiments also indicates the effective and accurate of the algorithms. And, the result of R clustering ca n be easily used for the later practice.展开更多
Assessment of temporal and spatial variations in surface water quality is important to evaluate the health of a watershed and make necessary management decisions to control current and future pollution of receiving wa...Assessment of temporal and spatial variations in surface water quality is important to evaluate the health of a watershed and make necessary management decisions to control current and future pollution of receiving water bodies. In this work, surface water quality data for 12 physical and chemical parameters collected from 10 sampling sites in the Nenjiang River basin during the years(2012-2013) were analyzed. The results show that river water quality has significant temporal and spatial variations. Hierarchical cluster analysis(HCA) grouped 12 months into three periods(LF, MF and HF) and classified 10 monitoring sites into three regions(LP, MP and HP) based on the similarity of water quality characteristics. The principle component analysis(PCA)/factor analysis(FA) was used to recognize the factors or origins responsible for temporal and spatial water quality variations. Temporal and spatial PCA/FA revealed that the Nenjiang River water chemistry was strongly affected by rock/water interaction, hydrologic processes and anthropogenic activities. This work demonstrates that the application of HCA and PCA/FA has achieved meaningful classification based on temporal and spatial criteria.展开更多
基金supported by the National Natural Science Foundation of China (70571087)the National Science Fund for Distinguished Young Scholars of China (70625005)
文摘Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.
文摘Hierarchical clustering analysis based on statistic s is one of the most important mining algorithms, but the traditionary hierarchica l clustering method is based on global comparing, which only takes in Q clusteri ng while ignoring R clustering in practice, so it has some limitation especially when the number of sample and index is very large. Furthermore, because of igno ring the association between the different indexes, the clustering result is not good & true. In this paper, we present the model and the algorithm of two-level hierarchi cal clustering which integrates Q clustering with R clustering. Moreover, becaus e two-level hierarchical clustering is based on the respective clustering resul t of each class, the classification of the indexes directly effects on the a ccuracy of the final clustering result, how to appropriately classify the inde xes is the chief and difficult problem we must handle in advance. Although some literatures also have referred to the issue of the classificati on of the indexes, but the articles classify the indexes only according to their superficial signification, which is unscientific. The reasons are as follow s: First, the superficial signification of some indexes usually takes on different meanings and it is easy to be misapprehended by different person. Furthermore, t his classification method seldom make use of history data, the classification re sult is not so objective. Second, for some indexes, its superficial signification didn’t show any mean ings, so simply from the superficial signification, we can’t classify them to c ertain classes. Third, this classification method need the users have higher level knowledge of this field, otherwise it is difficult for the users to understand the signifi cation of some indexes, which sometimes is not available. So in this paper, to this question, we first use R clustering method to cluste ring indexes, dividing p dimension indexes into q classes, then adopt two-level clustering method to get the final result. Obviously, the classification result is more objective and accurate. Moreover, after the first step, we can get the relation of the different indexes and their interaction. We can also know under a certain class indexes, which samples can be clustering to a class. (These semi finished results sometimes are very useful.) The experiments also indicates the effective and accurate of the algorithms. And, the result of R clustering ca n be easily used for the later practice.
基金Project(2012ZX07501002-001)supported by Major Science and Technology Program for Water Pollution Control and Treatment of the Ministry of Science and Technology,China
文摘Assessment of temporal and spatial variations in surface water quality is important to evaluate the health of a watershed and make necessary management decisions to control current and future pollution of receiving water bodies. In this work, surface water quality data for 12 physical and chemical parameters collected from 10 sampling sites in the Nenjiang River basin during the years(2012-2013) were analyzed. The results show that river water quality has significant temporal and spatial variations. Hierarchical cluster analysis(HCA) grouped 12 months into three periods(LF, MF and HF) and classified 10 monitoring sites into three regions(LP, MP and HP) based on the similarity of water quality characteristics. The principle component analysis(PCA)/factor analysis(FA) was used to recognize the factors or origins responsible for temporal and spatial water quality variations. Temporal and spatial PCA/FA revealed that the Nenjiang River water chemistry was strongly affected by rock/water interaction, hydrologic processes and anthropogenic activities. This work demonstrates that the application of HCA and PCA/FA has achieved meaningful classification based on temporal and spatial criteria.
