Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation

摘要

We define the measure of upper and the measure of lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive fuzzy relation R. In case when the relation R is also symmetric, these measures coincide and we call their value by the measure of roughness of rough approximation. Basic properties of such measures are studied. A realization of measures of rough approximation in terms of L-fuzzy topologies is presented.