Type-2 Fuzzy Sets as Functions on Spaces

Aisbett, Janet; Rickard, John T.; Morgenthaler, David G.

doi:10.1109/tfuzz.2010.2046176

Cited by 92 publications

(46 citation statements)

References 16 publications

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“…Therefore, the determination of the membership degree of each element to the set is the biggest problem for applying FS theory. Taking these considerations into account, the concept of type-2 fuzzy set was given as follows: A T2FS is a FS for which the membership degrees are expressed as FSs on [0,1].…”

Section: A Origin Of the Conceptmentioning

confidence: 99%

“…An easier notation, following the ideas in Aisbett, Rickard and Morgenthaler in [1], is the following one. Definition 4.6:…”

Section: Some Considerations About T2fssmentioning

confidence: 99%

“…As the set 2 [0,1] , with the classical definitions of union and intersection between (crisp) sets, is a bounded lattice, we have the following result.…”

Section: A Set-valued Fuzzy Setsmentioning

confidence: 99%

See 2 more Smart Citations

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

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show abstract

Section: A Origin Of the Conceptmentioning

confidence: 99%

“…An easier notation, following the ideas in Aisbett, Rickard and Morgenthaler in [1], is the following one. Definition 4.6:…”

Section: Some Considerations About T2fssmentioning

confidence: 99%

See 1 more Smart Citation

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

408

159

View full text Add to dashboard Cite

show abstract

“…Now we introduce a more modern definition: Definition: A Type-2 Fuzzy Set [24] is a bivariate function on the cartesian product…”

Section: Type-2 Fuzzy Logic Systemsmentioning

confidence: 99%

“…Definition [24]: The FOU is the union of all the primary memberships and is given by {(x, t) ∈ X × [0, 1]|µ(x, t) > 0}. As stated in [24] it is the support of µ.…”

Section: Type-2 Fuzzy Logic Systemsmentioning

confidence: 99%

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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References

2014

Introduction to Type‐2 Fuzzy Logic Control

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Type-2 Fuzzy Sets as Functions on Spaces

Cited by 92 publications

References 16 publications

A Historical Account of Types of Fuzzy Sets and Their Relationships

A Historical Account of Types of Fuzzy Sets and Their Relationships

Type-2 fuzzy elliptic membership functions for modeling uncertainty

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