Fuzzifying bornivorous sets of fuzzifying bornological linear spaces

Abstract

The main purpose of this paper is to introduce a notion of
 fuzzifying bornivorous sets of fuzzifying bornological linear
 spaces. In particular, we provide an example of fuzzifying
 bornivorous sets on a fuzzifying topological linear space with its
 von Neumann bornology. Furthermore, the description of fuzzifying
 open sets of fuzzifying bornological linear spaces is showed and its
 equivalent illustration is discussed as well. In addition, we study
 the dual relationship of fuzzifying open and close sets. The
 fuzzifying topological space induced by fuzzifying open sets is also
 discussed.