Leveraging IT2 Input Fuzzy Sets in Non-Singleton Fuzzy Logic Systems to Dynamically Adapt to Varying Uncertainty Levels

Abstract

Most real-world environments are subject to different sources of uncertainty which may vary in magnitude over time. We propose that while Type-1 (T1) Non-Singleton Fuzzy Logic System (NSFLSs) have the potential to tackle uncertainty within the input Fuzzy Sets (FSs), Type-2 (T2) input FSs provide the ability to also capture variation in uncertainty levels by means of their extra degrees of freedom. Specifically, in this paper, we propose a strategy to design Interval Type-2 (IT2) input Membership Functions (MFs) in an online manner to ensure the parameters of input MFs are updated dynamically, thus capturing varying levels of uncertainty affecting systems' inputs. In this strategy, first, uncertainty detection is performed over a given time-frame (the Uncertainty Estimation Time-frame) and Type-1 (T1) input MFs are constructed by utilising the detected uncertainty level. Second, the variation of the uncertainty levels over a sliding window (the Uncertainty Variation Window) is used to capture the degree of variation in the detected uncertainty levels over time, which in turn informs the size of the Footprint of Uncertainty (FOU) of the IT2 MF associated with the T1 principal MF. Using time-series prediction experiments as an initial evaluation and demonstration platform for the proposed architecture, we show that the proposed strategy of designing IT2 input MFs has the potential to deliver performance benefits. Specifically, it allows systems to not only adapt to specific uncertainty levels but also to be more resilient to the variation of said uncertainty levels over time, thus offering a pathway to robust performance in real-world applications.

Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems

“…Sahab and Hagras proposed an automatic generation of non-singleton type-2 fuzzy inputs from data without an assumption of a specific shape about the uncertainty distribution associated with the input [23]. Pekaslan et al presented a method for dynamic update of interval type-2 fuzzy input sets capturing varying levels of uncertainty affecting systems' inputs [18].…”