A New Distance-Type Fuzzy Inference Method Based on Characteristic Parameters

Abstract

Reasoning is a cognitive activity that leverages knowledge to generate solutions to problems. Knowledge representations in the brain require both symbolic and graphical information since visual information is figurative and conveys a large amount of information. Consequently, graphical knowledge representation is often employed in reasoning. Distance-type fuzzy inference utilizes the distance information between the antecedent and the set of facts as the basis for inference. Compared to Mamdani inference, the distance-type fuzzy inference method not only satisfies the convexity and asymptotic properties of the inference results but also adheres to the separation rule (modus ponens), a fundamental principle in inference. This paper discusses extensions of distance-type fuzzy inference methods to handle spatial figures. In this paper, we first explain the distance-type fuzzy inference method. Then, we discuss the concept representation in the feature space and independent parameters that can completely express the characteristics of a figure in space, which are defined as “characteristic parameters”. Furthermore, we describe the correspondence between figures and vectors in the feature space, propose a new distance-type fuzzy inference method based on characteristic parameters and describe its characteristics. Finally, an example is used to demonstrate the inference results of this new distance-type fuzzy inference method.