Classification based on L -fuzzy sets 1

Abstract

Partitions are at the basis of many processes as classification. They are classically defined in the context of crisp sets. However, partitions based on fuzzy sets have been proven to be more useful in real-life problems. This has motivated several different proposals to extend the definition of partition to the fuzzy sets context. Nevertheless, fuzzy sets evaluated in the real interval [0, 1] are still a too restrictive context for some problems. In this contribution we propose a generalization of the notion of partition based on lattices valued sets. We also study some of their properties.