Discussion on fuzzy decision making based on fuzzy number and compositional rule of inference

Abstract

This paper provides an improved decision making approach based on fuzzy numbers and the compositional rule of inference by Yao and Yao (2001). They claimed to have created a new method that combines statistical methods and fuzzy theory for medical diagnosis. Currently, numerous papers have cited that work. In this study, we show that if we follow their matrix multiplication operation approach, we will obtain the same result as the original method proposed by Klir and Yuan (1995). Owing to a wellknown property of (row) stochastic matrices, if the multiplication is closed, the fuzzy and defuzzy procedure of Yao and Yao (2001) is redundant. Therefore, we advise researchers to think twice before applying this approach to medical diagnosis.