Interval-based and fuzzy set-based approaches to modeling of fuzzy inference systems with the local monotonicity property

Even though the importance of the local monotonicity property for function approximation problems is well established, there are relative few investigations addressing issues related to the fulfillment of the local monotonicity property in Fuzzy Inference System (FIS) modeling. We have previously conducted a preliminary study on the local monotonicity property of FIS models, with the assumption that the extrema point(s) (i.e., the maximum and/or minimum point(s)) is either known precisely or totally unknown. However, in some practical situations, the extrema point(s) can be known imprecisely (as an interval or a fuzzy set). In this paper, the imprecise information is exploited to construct an FIS model that fulfills the local monotonicity property. A procedure to estimate the extrema point(s) of a function is devised. Applicability of the findings to a data-driven modeling problem is further demonstrated.