Abstract
The conventional fuzzy c-spherical shells (FCSS) clustering model is extended to cluster shells involving non-crisp numbers, in this paper. This is achieved by a vectorized representation of distance, between two non-crisp numbers like the crisp numbers case. Using the proposed clustering method, named vector fuzzy c-spherical shells (VFCSS), all crisp and non-crisp numbers can be clustered by the FCSS algorithm in a unique structure. Therefore, we can implement FCSS clustering over various types of numbers in a unique structure with only a few alterations in the details used in implementing each case. The relations of VFCSS applied to crisp and non-crisp (containing symbolic-interval, LR-type, TFN-type and TAN-type fuzzy) numbers are presented in this paper. Finally, simulation results are reported for VFCSS applied to synthetic LR-type fuzzy numbers; where the application of the proposed method in real life and in geomorphology science is illustrated by extracting the radii of circular agricultural fields using remotely sensed images and the results show better performance and lower cost computational complexity of the proposed method in comparison to conventional FCSS.
Highlights
Use of clustering models is a wide field of research in image processing and pattern recognition and they have been applied in different areas such as business, geology, engineering systems, etc. [1,2,3]
Since Zadeh [5] presented fuzzy sets which introduce the idea of partial membership of belonging defined by a membership function, fuzzy clustering has been applied in various areas
We can cluster non-crisp numbers that have spherical shells form using the proposed. These non-crisp numbers can be available, or we can produce them from proposed vector fuzzy c-spherical shells (VFCSS)
Summary
Use of clustering models is a wide field of research in image processing and pattern recognition and they have been applied in different areas such as business, geology, engineering systems, etc. [1,2,3]. Use of clustering models is a wide field of research in image processing and pattern recognition and they have been applied in different areas such as business, geology, engineering systems, etc. While the proposed method in this paper is objective-function based, generally clustering models may be objective-function, hierarchical or heuristic based. Hard clustering methods restrict each point of the data set to exactly one cluster [4]. Since Zadeh [5] presented fuzzy sets which introduce the idea of partial membership of belonging defined by a membership function, fuzzy clustering has been applied in various areas. Research in this field has been extended to apply fuzzy states to crisp cases. In the literature on fuzzy clustering, the fuzzy c-mean (FCM) clustering algorithms are the best-known methods [2,6]
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