NFI: A neuro-fuzzy inference method for transductive reasoning

This paper introduces a novel neural fuzzy inference method-NFI for transductive reasoning systems. NFI develops further some ideas from DENFIS-dynamic neuro-fuzzy inference systems for both online and offline time series prediction tasks. While inductive reasoning is concerned with the development of a model (a function) to approximate data in the whole problem space (induction), and consecutively-using this model to predict output values for a new input vector (deduction), in transductive reasoning systems a local model is developed for every new input vector, based on some closest to this vector data from an existing database (also generated from an existing model). NFI is compared with both inductive connectionist systems (e.g., MLP, DENFIS) and transductive reasoning systems (e.g., K-NN) on three case study prediction/identification problems. The first one is a prediction task on Mackey Glass time series; the second one is a classification on Iris data; and the last one is a real medical decision support problem of estimating the level of renal function of a patient, based on measured clinical parameters for the purpose of their personalised treatment. The case studies have demonstrated better accuracy obtained with the use of the NFI transductive reasoning in comparison with the inductive reasoning systems.