A LINEAR STRUCTURE AND CONVEXITY FOR RELATIONS IN DYNAMIC FUZZY-SYSTEMS

Introducing a linear structure for a fuzzy relation, we could Prove th e linearity of the fuzzy integral with respect to this relation. It is known that the fuzzy integral does not have the linearity, so this be comes an obstacle in developing the fuzzy dynamic system. To avoid thi s, we will impose some restrictive assumptions for a fuzzy relation de fined on the positive orthant of an n-dimensional Euclidean space. Als o, fuzzy Markov decision processes with deterministic stationary polic ies are formulated and its characterization is given by a recursive eq uation in the fuzzy state.