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

Direnc Pekaslan,Jonathan M. Garibaldi,Christian Wagner

doi:10.1109/fuzz-ieee.2019.8858800

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.

Highlights

The real-world encompasses different noise sources and these sources may affect system inputs at different levels
The variation of the stored uncertainty levels is captured over a sliding window and utilised to construct an Footprint of Uncertainty (FOU) which is associated with the T1 Membership Functions (MFs), resulting in an Interval Type-2 (IT2) input MF
We investigate that which FOU value in IT2 input MFs provides the least prediction error and how does this compare to the proposed adaptive approach

Summary

Introduction

The real-world encompasses different noise sources and these sources may affect system inputs at different levels While these noise sources may vary vastly and cause either major or minor impact on a system’s inputs. Non-Singleton Fuzzification is useful in cases where the system inputs are affected by an external factor which causes a distortion in the actual input. To capture this distortion, inputs are designed as Non-Singleton FSs. Conceptually, in Non-Singleton fuzzification, it is commonly assumed that the crisp input x is likely to be correct value, but that because of existing uncertainty, neighbouring values of x have potential to be the accurate values. The equation of a Gaussian Nonsingleton input MFs is commonly used to model NS input MFs:

Methods

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Conclusion