Fuzzy Sets and Fuzzy Partitions
In this paper some connections between a characterization of fuzzy sets and a characterization of fuzzy partitions are explored. We extend the notion of α-level set and sharpness of fuzzy sets to fuzzy partitions. Then we define α-level equivalence and relation of sharpness on the set of all fuzzy partitions of a finite set of objects into k clusters. We define sharpnesshood and complementhood of fuzzy partitions and then we show how to find the complement of a fuzzy partition.
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