Triangular norm based graded convex fuzzy sets

In this paper, we develop the theory of graded convex fuzzy set, graded strongly convex fuzzy set, graded strictly convex fuzzy set based on triangular norms, in which the degree of fuzzy convexity is described by one real number. We also investigate some graded properties of these graded convex fuzzy sets and present the relations between these graded convex fuzzy sets and their topological properties and give several conditions for a fuzzy set to be a graded convex fuzzy set. Finally, we generalize the notion of global maximizer and prove an important property of graded convex fuzzy sets.