Fuzzy learning under and about an unfamiliar fuzzy teacher

This study addresses the problem of optimal parametric learning in unfamiliar fuzzy environments. Prior studies in the domain of unfamiliar environments, which employed either crisp or fuzzy approaches to model the uncertainty or imperfectness of the learning environment, assumed that the training sample labels provided by the unfamiliar teacher were crisp, even if not perfect. Here, the more realistic problem of fuzzy learning under an unfamiliar teacher who provides only fuzzy (instead of crisp) labels, is tackled by expanding the previously defined fuzzy membership concepts to include an additional component representative of the fuzziness of the teacher. The previously studied scenarios, namely, crisp and fuzzy learning under (crisp) unfamiliar teacher, can be looked upon as special cases of this new methodology. As under the earlier studies, the estimated membership functions can then be deployed during the ensuing classification decision phase to judiciously take into account the imperfectness of the learning environment. The study also offers some insight into the properties of several of these fuzzy membership function estimators by examining their behavior under certain specific scenarios.