Exploring Subsethood to Determine Firing Strength in Non-Singleton Fuzzy Logic Systems

摘要

Real world environments face a wide range of sources of noise and uncertainty. Thus, the ability to handle various uncertainties, including noise, becomes an indispensable element of automated decision making. Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to tackle uncertainty within the design of fuzzy systems. The firing strength has a significant role in the accuracy of FLSs, being based on the interaction of the input and antecedent fuzzy sets. Recent studies have shown that the standard technique for determining firing strengths risks substantial information loss in terms of the interaction of the input and antecedents. Recently, this issue has been addressed through exploration of alternative approaches which employ the centroid of the intersection (cen-NS) and the similarity (sim-NS) between input and antecedent fuzzy sets. This paper identifies potential shortcomings in respect to the previously introduced similarity-based NSFLSs in which firing strength is defined as the similarity between an input FS and an antecedent. To address these shortcomings, this paper explores the potential of the subsethood measure to generate a more suitable firing level (sub-NS) in NSFLSs featuring various noise levels. In the experiment, the basic waiter tipping fuzzy logic system is used to examine the behaviour of sub-NS in comparison with the current approaches. Analysis of the results shows that the sub-NS approach can lead to more stable behaviour in real world applications.