Gradation of supra-openness

In 1992 a new definition of a fuzzy topological space was given by Chattopadhyay et al. (1992) by introducing the concept of a gradation of openness. In this paper a new definition of a fuzzy supra-topological (resp. supra-proximity, supra uniform) space is given by introducing the concept of a gradation of supra-openness (resp. supra-proximity, supra-uniformity) on a non-empty set X. How to construct a gradation of supra-openness induced by a gradation of supra-proximity (resp. supra-uniformity) is explained. The connection between gradations of supra-proximity and gradations of supra-uniformity are investigated. Throughout this paper, the class of all fuzzy subsets on a non-empty set X will be denoted by I-X and fuzzy subsets will be denoted by small Greek letters. Also, we identify each subset with its characteristic function. (C) 2000 Elsevier Science B.V. All rights reserved. AMS subject classification: 54 A 40.