OPERATIONS OF FUZZY BORNOLOGIES AND THEIR PROPERTIES(II)
Lei Ying-jie · Journal of Shaanxi University of Science & Technology · 2009
On the basis of Hogbe-Nlend.H's definition of a bornology a conception of a fuzzy bornological spaces is defined,two new operations(internal union and intersection)of families of fuzzy subsets of an arbitrary universe are introduced and a pilot study is given to their fundamental properties.The following results are obtained:(1)a normal and finite bornological space is trivial;(2)there exist a smallest fuzzy bornology and a smallest normal fuzzy bornology;(3)either of the family of all the fuzzy bornologies and the family of all the normal fuzzy bornologies forms a monoid with internal union as a binary operation;(4)either of the families mentioned before is closed under the intersection of any of their own nonempty subfamilies.