Contrasting singleton type-1 and interval type-2 non-singleton type-1 fuzzy logic systems

Aladi, Jabran Hussain; Wagner, Christian; Pourabdollah, Amir

Abstract

Most applications of both type-1 and type-2 fuzzy logic systems are employing singleton fuzzification due to its simplicity and reduction in its computational speed. However, using singleton fuzzification assumes that the input data (i.e., measurements) are precise with no uncertainty associated with them. This paper explores the potential of combining the uncertainty modelling capacity of interval type-2 fuzzy sets with the simplicity of type-1 fuzzy logic systems (FLSs) by using interval type-2 fuzzy sets solely as part of the non-singleton input fuzzifier. This paper builds on previous work and uses the methodological design of the footprint of uncertainty (FOU) of interval type-2 fuzzy sets for given levels of uncertainty. We provide a detailed investigation into the ability of both types of fuzzy sets (type-1 and interval type-2) to capture and model different levels of uncertainty/noise through varying the size of the FOU of the underlying input fuzzy sets from type-1 fuzzy sets to very “wide” interval type-2 fuzzy sets as part of type-1 non-singleton FLSs using interval type-2 input fuzzy sets. By applying the study in the context of chaotic time-series prediction, we show how, as uncertainty/noise increases, interval type-2 input fuzzy sets with FOUs of increasing size become more and more viable.

Citation

Aladi, J. H., Wagner, C., & Pourabdollah, A. (2016). Contrasting singleton type-1 and interval type-2 non-singleton type-1 fuzzy logic systems.

• Conference Name: 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2016)
• End Date: Jul 29, 2016
• Acceptance Date: May 10, 2016
• Publication Date: Jul 24, 2016
• Deposit Date: Aug 4, 2017
• Publicly Available Date: Aug 4, 2017
• Peer Reviewed: Peer Reviewed
• Keywords: Time series analysis, Fuzzy logic, Signal to noise ratio, Noise measurement
• Public URL: https://nottingham-repository.worktribe.com/output/799717
• Publisher URL: http://ieeexplore.ieee.org/document/7737943/
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• Contract Date: Aug 4, 2017