On convexity of fuzzy syntopogenous spaces

In this paper, we combine fuzzy syntopogenous structures with algebraic on X, and look for their corresponding structures and typical properties. First, the *-increasing and *-decreasing spaces have been studied and an important example (R-phi, S-R, less than or equal to) has been given (Theorem 3.10). Second, two general types of convexity on L-fuzzy syntopogenous structures (X, S, less than or equal to) have been defined, the examples of them have been given and their relationship has been investigated. Third, the equivalent description of convexity have been given. Finally, a sequence of important properties of convexity have been obtained. (C) 2002 Elsevier Science B.V. All rights reserved.