Affiliations: [a] Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
| [b] Department of Mathematics, Payam Noor University, Shiraz Branch, Shiraz, Iran
Correspondence:
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Corresponding author. Alireza Fakharzadeh Jahromi, Department of Mathematics, Shiraz University of Technology,
Shiraz, Iran. Tel.: +989173173320; Fax: +987137354500; E-mail: [email protected].
Abstract: Regarding the magnificent ability of the fuzzy logic in explanation and analyzing the real phenomena, using fuzzy data is growing rapidly. But the tools for doing data mining in a fuzzy data set; especially in high dimension, are not sufficient. Considering the remarkable ability of the LoOP (Local Outlier Probabilities) method in outlier detecting in high dimensional crisp data set, like supplying for each data object, determining outlier probability as scar which is easily explainable competitor on various synthetic and real world data sets, the aim of this article is to present an extended version of this method for using in high dimensional fuzzy database. In order to provide a completely fuzzy strategy, first we propose a new approach to assigning distance between fuzzy high dimension data based on Hausdorff and Vertex distance. After proving that this distance measuring is a metric, since LoOP is a distance based method, we redefined the LoOP algorithm step by step based on the new meter. Then we allocate an outlier score in the range of [0,1] to each data based on LoOP idea, to identify the outliers. The presented numerical tests show the efficiency of the new method, for random cases of knowing and unknowing the outlier and a real case. The results shows also the stability and robustness of the presented method more that its accuracy.
