On the independence of fuzzy vectors

Fuzzy variable is a function from a possibility space to the real line. By analogy of the independence of random variables, there are similar terms for fuzzy variables such as unrelated fuzzy variables, noninteractive fuzzy variables, and independent fuzzy variables. The purpose of this work is to discuss the relations among these terms. Toward this end, the work first defines the marginal possibility distributions of a fuzzy vector, and then gives a simple approach to define the independent fuzzy variables. After that, the equivalence of unrelated, noninteractive, and independent fuzzy variables are proved in the framework of possibility theory.