Monotone fuzzy control method and its control performance

For most process controls the relation between the input and the output is of monotonicity. So a question immediately arises as follows: For two precise inputs, say x⩽y, can the fuzzy control method guarantee the corresponding crisp outputs preserving the same inequality? Or whether or not the fuzzy control method is of monotone? In this paper, we will focus on the problems mentioned above. Therefore, some new concepts about this topic are proposed, such as the monotone and the rough monotone control algorithm, the monotone rule base and the monotone smooth transition system model, etc. Analysis shows that as long as the rule base is monotone, the single-input single-output conventional Mamdani fuzzy control algorithm (CMFCA for short) is monotone and the two-input single-output CMFCA is rough monotone. Finally, a sufficient condition for monotonicity of the CMFCA is obtained, i.e. if the rule base is monotonic and the universes is partitioned by isosceles triangle fuzzy numbers with base point single resonating, then the two-input single-output conventional Mamdani algorithm is of monotone