Fuzzy convex sets in median algebras (Q1847597)

A ternary algebra \textbf{A} (with the ternary operation \( (a,b,c) \rightarrow [a,b,c]\)) is called a median algebra if it satisfies the following identities: \( [aab] = a , [abc]=[bac]=[bca] , [[abc]de] = [a[bde][cde]]\). In this paper the fuzzification of convex sets in median algebras is considered,and some of their properties are investigated. Also, a characterization of finite-valued fuzzy convex sets is given.