The fuzzy intersection rule in variational analysis with applications

The fuzzy intersection rule for Fréchet normal cones in Asplund spaces was established by Mordukhovich and the author using the extremal principle, which appears more convenient to apply in some applications. In this paper, we present a complete discussion of this rule in various aspects. We show that the fuzzy intersection rule is another characterization of the Asplund property of the space. Various applications are considered as well. In particular, a complete set of fuzzy calculus rules for general lower semicontinuous functions are established.