Abstract
In this paper, a generalized fuzzy compatibility relation between two universes is defined. By a generalized fuzzy compatibility relation between two universes, a covering and a tolerance relation are induced to a single universe. Based on the above covering and tolerance relation, the new extended patterns of three types of fuzzy rough set models on two universes are proposed. An important common characteristic of these new extended patterns is that the new approximation operators can be obtained by the composition of the approximation operators and the inverse approximation operators. We mainly construct the new extended models of fuzzy rough sets, -fuzzy rough sets and -fuzzy rough sets on two universes and investigate their properties.
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