Fuzzifying bornivorous sets of fuzzifying bornological linear spaces

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.