Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making

This paper presents a case study in which the introduction of vagueness or uncertainty into the membership functions of a fuzzy system was investigated in order to model the variation exhibited by experts in a medical decision-making context. A conventional (type-1) fuzzy expert system had previously been developed to assess the health of infants immediately after birth by analysis of the biochemical status of blood taken from infants\´ umbilical cords. Variation in decision making was introduced into the fuzzy expert system by means of membership functions which altered in small, predetermined manners over time. Three types of variation in membership functions were investigated: i) variation in the centre points, ii) variation in the widths, and iii) the addition of "white noise". Different levels (amounts) of uniformly distributed random variation were investigated for each of these types. Monte Carlo simulations were carried out to propagate the variation through the inferencing process in order to determine distributions of the conclusions reached. Interval valued type-2 fuzzy systems were also implemented to investigate the boundaries of variability in decisions. The results obtained were compared to the experts\´ decisions in order to determine which type and size of membership function variability best matched the experts\´ variability. The novel reasoning technique introduced in this study is termed nonstationary fuzzy reasoning