Fuzzy vectors as a tool for modeling uncertain multidimensional quantities

The paper deals with modeling uncertain multidimensional quantities by means of fuzzy vectors. In connection with possible interactions among variables, the separability of fuzzy vectors is discussed in detail. For the case when interconnections among variables are given by a crisp relation, a more general form of separability of fuzzy vectors—the separability on a given relation (e.g. on a probability simplex) is introduced. Properties of fuzzy vectors separable on a given relation are studied, and ways of convenient setting of such fuzzy vectors are proposed. Finally, fuzzy extensions of real-valued functions and real-vector-valued functions to general input fuzzy vectors are investigated.