Abstract

In this paper, we establish new definitions of smooth closure and smooth interior of a fuzzy set [3] under the name of fuzzy closure and fuzzy interior of a fuzzy set which satisfy almost all properties of the corresponding definitions in fuzzy topological spaces in Chang's sense. As a consequence of these definitions we show that the topological concepts, especially various types of compactness, can be presented in a simple way, with no additional hypotheses needed which occured in [3] and with no counterpart in [2, 4, 6].

Keywords: Smooth closure, smooth interior, fuuzy topological space.

MSC: 54A40, 54D30

Pages:  75$-$81     

Volume  50 ,  Issue  3$-$4 ,  1998