This paper presents a general framework for the study of fuzzy rough sets in which constructive approach is used. In the approach, a pair of lower and upper general fuzzy rough approximation operator in the lattice L is defined. Furthermore, the entire property and connection between the set of logical operator and the set of its corresponding general fuzzy rough approximation operator are examined, and we prove that they are 1-1 mapping. In addition, the structural theorem of negator operator is given. At last, the decomposition and synthesize theorem of general fuzzy rough approximation operator are proved. That for how to promote general rough approximation operator to suitable general fuzzy rough approximation operator, that is, how to select logical operator, provides theory foundation.
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