Fuzzy Clustering Approaches Based On AFS Fuzzy Logic

AFS (Axiomatic Fuzzy Set) theory was proposed first as a new analytic method of fuzzy mathematics. In the framework of AFS theory, the membership functions and their logic operations for fuzzy concepts can be impersonally determined according to original data and facts. AFS theory has been applied to data mining, pattern recognition and failure diagnosis.Professor Liu proposed AFS Fuzzy logic clustering algorithm (X.D. Liu, W.Wang and T.Y.Chai. IEEE Transaction on Systems, Man, Cybernetics, 2005). Experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data effectively, and find an optimal number of clusters. However, its shortcoming is the approach to find the fuzzy description of each sample is a little bit rough, and just the examples which have less than 10 samples were applied by Professor Liu. Aiming at this problem, we improve the AFS Fuzzy logic clustering algorithm and apply the improved algorithm to well known real-world Iris data (reference ftp://ftp.ics.uci.edu/pub/machine-learning-databases/Iris/). In stead of examples of less than 10 samples, we apply the improved algorithm to the well known real-world Iris data which has 150 samples.It is well known that feature selection is very important for clustering. Because some features can be just "noise", not contributing to (or even degrading) the clustering process. So the task of selecting the "best" feature subset can improve the performance of most clustering algorithms. Thus in this paper, based on the fuzzy implicator, an algorithm of selecting optimal subsets of relevant features for fuzzy clustering is proposed. Thus a new fuzzy clustering algorithm based on AFS theory is achieved. Finally, the proposed clustering algorithm is applied to the well known real-world wine data set.In this paper's application, just the order relationships of the samples on the attributes are used. Experimental results demonstrate that a high clustering accuracy can be obtained by the proposed clustering algorithm only accordingto the order relations of...