Exploring Zadeh's General Type-2 Fuzzy Logic Systems for Uncertainty Quantification

Yusuf Guven, Ata Koklu, Tufan Kumbasar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This article introduces an exploration of general Type-2 (GT2) fuzzy logic systems (FLSs) via Zadeh's (Z) GT2 fuzzy set (FS) definition, with a strong emphasis on advancing uncertainty quantification (UQ). At the heart of our contribution is the introduction of Z-GT2-FLS, formed through the integration of Z-GT2-FS with the α-plane representation. We show that the design flexibility of GT2-FLS is increased as it takes away the dependency of the secondary membership function definition from the primary membership function. For learning, we provide a solution to the curse of dimensionality problem alongside a method to seamlessly integrate deep learning (DL) optimizers. This article further presents a dual-focused Z-GT2-FLS within a DL framework, intending to learn Z-GT2-FLSs that are capable of achieving high-quality prediction intervals alongside high precision. In this context, we assign distinct roles for αk-plane-associated interval type-2 FLSs through a composite loss function. In addition, we extend the application of Z-GT2-FLS to predictive distribution estimation, proposing a DL framework to learn the inverse cumulative distribution function by predicting entire quantile levels. We first reformulate the output of Z-GT2-FLS to represent a quantile level function, thereby offering flexibility in generating desired quantiles through α-planes. For learning, we propose a simultaneous quantile learning method alongside an adaptation mechanism to enhance learning performance. Through comparative analyses, we show that the Z-GT2-FLS excels in UQ compared to its fuzzy and DL counterparts. The contributions of this study underscore the versatility and superior performance of Z-GT2-FLS, positioning it as a valuable tool for UQ.

Original languageEnglish
Pages (from-to)314-324
Number of pages11
JournalIEEE Transactions on Fuzzy Systems
Volume33
Issue number1
DOIs
Publication statusPublished - 2025

Bibliographical note

Publisher Copyright:
© 1993-2012 IEEE.

Keywords

  • Accuracy
  • deep learning (DL)
  • design flexibility
  • general type-2 (GT2) fuzzy sets (FSs)
  • prediction interval (PI)
  • uncertainty quantification (UQ)

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