Partial Defuzzification of Fuzzy Clusters
Two methods of partial defuzzification of fuzzy clusters in a fuzzy k-partition are proposed. The first method is based on sharpening of fuzzy clusters with respect to the threshold 1/k. Sharpening is accomplished by application of the generalized operator of contrast intensification of fuzzy sets to k — 1 fuzzy clusters. The second method utilizes the idea of strong sharpening. In this approach the very small membership grades in each fuzzy cluster are reduced to zero. It is explained how these methods can lead to the well known approximation of a fuzzy partition by its crisp maximum membership partition.
KeywordsFuzzy Cluster Membership Grade Fuzzy Partition Maximum Membership Fuzzy Objective Function
Unable to display preview. Download preview PDF.
- BEZDEK, J.C. (1987): Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York.Google Scholar
- BODJANOVA, S. (2001): Operators of Contrast Modification of Fuzzy Sets. In: Proceedings of Joint 9th IFSA World Congress and 20th NAFIPS International Conference, IEEE, Vancouver, 1478–1483.Google Scholar
- JANG, J.-S.R, SUN, C.T. and MIZUTANI, E. (1997) Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence. Prentice Hall, Upper Saddle River.Google Scholar