J. Tayyebi - Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran.
E. Hosseinzadeh - Department of Mathematics, Kosar University of Bojnord, Bojnord, Iran.

The fuzzy c-means clustering algorithm is a useful tool for clustering; but it is convenient only for crisp complete data. In this article, an enhancement of the algorithm is proposed which is suitable for clustering trapezoidal fuzzy data. A linear ranking function is used to define a distance for trapezoidal fuzzy data. Then, as an application, a method based on the proposed algorithm is presented to cluster incomplete fuzzy data. The method substitutes missing attribute by a trapezoidal fuzzy number to be determined by using the corresponding attribute of q nearest-neighbor. Comparisons and analysis of the experimental results demonstrate the capability of the proposed method.

Fuzzy c-means algorithm, Incomplete data, Fuzzy data, Ranking function