Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

Wu, Dongrui

doi:10.1109/fuzz-ieee.2012.6251210

Cited by 80 publications

(36 citation statements)

References 68 publications

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“…There are some attempts to which type-2 MFs are the best for which application. For instance, in [27], a detailed analysis has been done on Gaussian and trapezoidal MFs in interval type-2 fuzzy logic controllers. It has been reported that interval type-2 fuzzy logic controllers by using Gaussian MFs are simpler in design, always continuous and faster for small rule-bases, whereas the controllers by using trapezoidal MFs are simpler in analysis [27].…”

Section: Type-2 Fuzzy Logic Systemsmentioning

confidence: 99%

“…For instance, in [27], a detailed analysis has been done on Gaussian and trapezoidal MFs in interval type-2 fuzzy logic controllers. It has been reported that interval type-2 fuzzy logic controllers by using Gaussian MFs are simpler in design, always continuous and faster for small rule-bases, whereas the controllers by using trapezoidal MFs are simpler in analysis [27]. Another path in research is the auto-generation of fuzzy MFs [28], however, the interpretation of these methods is still limited.…”

Section: Type-2 Fuzzy Logic Systemsmentioning

confidence: 99%

“…Since all operations on an interval type-2 fuzzy can be defined by operations on the upper and lower MFs as defined by (27) and (28):…”

Section: Additionmentioning

confidence: 99%

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Type-2 fuzzy elliptic membership functions for modeling uncertainty

Kayacan

Sarabakha

Coupland

et al. 2018

Engineering Applications of Artificial Intelligence

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Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance with existing type-2 fuzzy MFs. Furthermore, fuzzy arithmetic operations are also investigated, and our finding is that the elliptic MF has similar features to the Gaussian and triangular MFs in addition and multiplication operations. Moreover, we have tested the prediction capability of elliptic MFs using interval type-2 fuzzy logic systems on oil price prediction problem for a data set from 2nd Jan 1985 till 25th April 2016. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem of a quadrotor. We believe that the results of this study will open the doors to elliptic MFs' wider use of real-world identification and control applications as the proposed MF is easy to interpret in addition to its unique features.

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Section: Type-2 Fuzzy Logic Systemsmentioning

confidence: 99%

Section: Type-2 Fuzzy Logic Systemsmentioning

confidence: 99%

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Type-2 fuzzy elliptic membership functions for modeling uncertainty

Kayacan

Sarabakha

Coupland

et al. 2018

Engineering Applications of Artificial Intelligence

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“…However, IT2-FLCs are difficult to analyze and design since their internal structure is typically more complex than their type-1 counterpart [12]. In this context, several studies have been performed in order to design the IT2-FLCs [13][14][15]. Nevertheless, a systematic design for type-2 fuzzy controllers is still a challenging problem due to the main difficulty in determining the IT2-FSs and rulebase.…”

Section: Introductionmentioning

confidence: 99%

A big bang-big crunch optimization based approach for interval type-2 fuzzy PID controller design

Kumbasar

Hagras

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Abstract-In this paper, we will present a big bang-big crunch optimization (BB-BC) based approach for the design of an interval type-2 fuzzy PID controller. The implemented global optimization algorithm has a low computational cost and a high convergence speed. As a consequence, the BB-BC method is a very efficient search algorithm when the number of the optimization parameters is relatively big. The optimized type-2 fuzzy controller is compared with PID and type-1 fuzzy PID controllers which were optimized with either the BB-BC optimization method or conventional design strategies. The paper will also show the effect the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets on the closed loop system performance. We will present a comparative study performed on the highly nonlinear cascaded tank process to show the superiority of the optimized interval type-2 fuzzy PID controller compared to its optimized PID, type-1 counterparts.

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“…There is still a lot of research need as to which type-2 MFs are best for which application. In [9], a detailed analysis has been done on Gaussian and trapezoidal MFs in interval type-2 fuzzy logic controllers. It has been reported that interval type-2 fuzzy logic controllers by using Gaussian MFs are simpler in design, always continuous and faster for small rulebases, whereas the controllers by using trapezoidal MFs are simpler in analysis [9].…”

Section: Existing Type-2 Mfs In the Literaturementioning

confidence: 99%

Elliptic membership functions and the modeling uncertainty in type-2 fuzzy logic systems as applied to time series prediction

Kayacan

Coupland

John

et al. 2017

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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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. Abstract-In this paper, our aim is to compare and contrast various ways of modeling uncertainty by using different type-2 fuzzy membership functions available in literature. In particular we focus on a novel type-2 fuzzy membership function, -"Elliptic membership function". After briefly explaining the motivation behind the suggestion of the elliptic membership function, we analyse the uncertainty distribution along its support, and we compare its uncertainty modeling capability with the existing membership functions. We also show how the elliptic membership functions perform in fuzzy arithmetic. In addition to its extra advantages over the existing type-2 fuzzy membership functions such as having decoupled parameters for its support and width, this novel membership function has some similar features to the Gaussian and triangular membership functions in addition and multiplication operations. Finally, we have tested the prediction capability of elliptic membership functions using interval type-2 fuzzy logic systems on US Dollar/Euro exchange rate prediction problem. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic membership functions have comparable prediction results when compared to Gaussian and triangular membership functions.

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Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

Cited by 80 publications

References 68 publications

Type-2 fuzzy elliptic membership functions for modeling uncertainty

Type-2 fuzzy elliptic membership functions for modeling uncertainty

A big bang-big crunch optimization based approach for interval type-2 fuzzy PID controller design

Elliptic membership functions and the modeling uncertainty in type-2 fuzzy logic systems as applied to time series prediction

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