Abstract
This paper selects a residuated lattice L as the truth value table and selects a fixed element β∈L as the degree criterion, we introduce concepts of β-fuzzy equivalence relations and β-fuzzy partitions. The β-fuzzy partition is a natural generalization of fuzzy β-coverings. It is shown that they are one-to-one corresponding if and only if β=1. In order to check the reasonableness of β-fuzzy partitions, we define a pair of fuzzy upper/lower rough approximation operators and show that each of them has two equivalent descriptions, which is not possessed by fuzzy β-coverings.
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