Similarity relations, fuzzy partitions, and fuzzy orderings
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy partitions with the connectives T∞,S∞
Fuzzy Sets and Systems
The entropy of fuzzy dynamical systems and generators
Fuzzy Sets and Systems
Fuzzy Sets and Systems
One-to-one correspondences between ɛ-partitions, (1 - ɛ)-equivalences and ɛ-pseudometrics
Fuzzy Sets and Systems
Information Sciences: an International Journal
I-Fuzzy equivalence relations and I-fuzzy partitions
Information Sciences: an International Journal
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In this paper we study the behaviour of a kind of partitions formed by fuzzy sets, the @e-partitions, with respect to three important operations: refinement, union and product of partitions. In the crisp set theory, the previous operations lead to new partitions: every refinement of a partition is also a partition; the union of partitions of disjoint sets is a partition of the union set; the product of two partitions of two sets is a partition of the intersection of the partitioned sets. It has been proven that @e-partitions extend the three previous properties when the intersection of fuzzy sets is defined by the minimum t-norm and the union by the maximum t-conorm. In this paper we consider any t-norm defining the intersection of fuzzy sets and we characterize those t-norms for which refinements, unions and products of @e-partitions are @e-partitions. We pay special attention to these characterizations in the case of continuous t-norms.