SOLUTIONS TO FUZZY DIFFERENTIAL EQUATIONS: WEAKNESS AND POSSIBLE IMPROVEMENTS

摘要

We study and compare several approaches to ordinary differentialrnequations for systems with a fuzzy state. TwornODE problems in 2D, the first linear, the second nonlinear,rnserve as examples to illustrate the concepts. We showrnthat the existence of periodic solutions, which is given inrnthe crisp case, is lost for fuzzy formulations. Possible improvementrnof the fuzzy approach by applying the conceptrnof ordered fuzzy number theory as new generalization ofrnconvex fuzzy numbers, is proposed.