Improved Uncertainty Capture for Nonsingleton Fuzzy Systems

Abstract

(2016) Improved uncertainty capture for non-singleton fuzzy systems. IEEE Transactions on Fuzzy Systems, 24 (6). pp. 1513 -1524 . ISSN 1941 Access from the University of Nottingham repository: http://eprints.nottingham.ac.uk/45444/1/Improved%20Uncertainty%20Capture%20for %20Non-Singleton%20Fuzzy%20Systems.pdf Copyright and reuse:The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence. For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdf A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk 1 Improved Uncertainty Capture for Non-Singleton Fuzzy SystemsAmir Pourabdollah, Member, IEEE, Christian Wagner, Senior Member, IEEE, Jabran Hussain Aladi, Student Member, IEEE and Jonathan M. Garibaldi, Member, IEEE Abstract-In non-singleton fuzzy logic systems (NSFLSs), input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both: the appropriate modelling in the input fuzzy sets of the uncertainties present in the system's inputs, and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and thus affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed, and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input's uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time series predictions, where the NSFLSs' inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared to the standard approach.

A new dynamic approach for non-singleton fuzzification in noisy time-series prediction

“…[5], [13]) but the absolute results may not be directly compared, due to the significant effect of the experiment settings on the results. However in a similar setting used in [19] and [20], it is shown that the MSE of the standard NSFLS in 10dB noise has dropped by 28.15% and 7.71% when two alternative inference methods are applied (namely Cen-Min and Similarity-based, respectively). The 10.41% improvement of MSE shown in this paper is in parallel with (and potentially can be added to) the above improvements since it does not touch the inference engine, rather changes the fuzzification method.…”

“…the sup-star (e.g. maxmin) operation between the input and the antecedent MFs, it is suggested in [19] to use the centroid operator, and in [20] to use the MF's quantified similarities instead of the standard composition in the inference engine of NSFLSs used for noisy time-series prediction.…”

A comparative study on the control of quadcopter UAVs by using singleton and non-singleton fuzzy logic controllers

“…In spite of Sta-NSFLC is capable of handling uncertainties by capturing them from inputs, the adopted prefiltering approach in the Sta-NSFLC does not offer a fine-grained uncertainty information tracking, i.e., the prefilter is not highly sensitive to the shape of the input of FSs, leading to significant loss of information regarding the intersection of input and antecedent models. Therefore, an alternative type of the NSFLC initially developed in [14], [15], i.e.,Cen-NSFLC, has been developed for controlling the quadcopter UAV. In [14], [15], the novel approach to NSFLCs showed promising results in the context of time-series prediction with different levels of injected uncertainty.…”

“…Therefore, an alternative type of the NSFLC initially developed in [14], [15], i.e.,Cen-NSFLC, has been developed for controlling the quadcopter UAV. In [14], [15], the novel approach to NSFLCs showed promising results in the context of time-series prediction with different levels of injected uncertainty. The aim of the work discussed in this paper is to move beyond simulated levels of uncertainty to real-world uncertainty affecting real world sensors.…”

“…As detailed in [14], [15], the centroid of the intersection of an input X and an antecedent A, i.e. centroid of X ∩ A, the new input/output mapping is defined as:…”