Analysis and design of monotonic type-2 fuzzy inference systems

The prior knowledge-monotonicity property-is helpful for system analysis, modeling and design, especially when no specific physical structure knowledge about systems is available. This paper presents how to use interval type-2 fuzzy logic systems (IT2FLSs) to incorporate the monotonicity property into system design. First, we present sufficient conditions on the parameters of IT2FLSs to ensure the monotonicity between the inputs and outputs of IT2FLSs. Then, we transform the design of monotonic IT2FLSs to the least squares problem with linear-inequality constraints. At last, simulations are given to show the usefulness of the monotonicity property and the advantages of monotonic IT2FLSs under noisy circumstances.