Convex (s,t]-fuzzy sets and convex R -fuzzy sets

Following the Rosedfeld approach in investigating convex fuzzy sets, two new kinds of definitions of convex fuzzy sets are proposed in this paper. First, by the use of the relations between fuzzy points and fuzzy subsets, the definition of a convex (s,t]-fuzzy sets is introduced and their properties are discussed. The acceptable non-trivial concepts obtained in this manner are the convex (∈,∈νq) -fuzzy sets and convex (∈̅,∈̅νq̅)-fuzzy sets. Second, by the use of the implication operators of fuzzy logic, the convex R -fuzzy sets is proposed and the relations between the convex (s,t] -fuzzy sets and convex R -fuzzy sets are discussed.