A New Insight on the Mappings of Type-2 Fuzzy Logic Systems

Tufan Kumbasar

doi:10.1109/FUZZ-IEEE.2019.8858980

A New Insight on the Mappings of Type-2 Fuzzy Logic Systems

Tufan Kumbasar^*

^*Corresponding author for this work

Department of Control and Automation Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we provide a new insight on the mappings of Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) in comparison to its Type-1 (T1) counterparts. For the sake of simplicity, we focus on Single input IT2 (SIT2) FLSs that employ the Karnik Mendel (KM) or the Nie-Tan (NT) Centre of Sets Calculation Method (CSCM). Through theoretical investigations, it is shown that there does exist an equivalent SIT2-FLS representation with a Single input T1 (ST1) FLS that uses Rational Polynomial Functions (RBFs) in their rule consequents. It is concluded that SIT2-FLSs cannot be implemented with traditional ST1-FLSs. It is also revealed that the extra degree of freedom provided by IT2 fuzzy sets and CSCM results with RBFs that can generate much more complex mapping when compared to its T1 counterparts. It is also proven that SIT2-FLSs can be seen as adaptive ST1-FLSs that are tuned via a collection of ST1-FLSs. Thus, SIT2-FLSs have adaptive feature property that does not exists in ST1-FLSs. It is also shown that the SIT2-FLS employing the KM is more complex but also capable to accommodate a much wider range of mappings when compared its NT counterpart.

Original language	English
Title of host publication	2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781538617281
DOIs	https://doi.org/10.1109/FUZZ-IEEE.2019.8858980
Publication status	Published - Jun 2019
Event	2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019 - New Orleans, United States Duration: 23 Jun 2019 → 26 Jun 2019

Publication series

Name	IEEE International Conference on Fuzzy Systems
Volume	2019-June
ISSN (Print)	1098-7584

Conference

Conference	2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019
Country/Territory	United States
City	New Orleans
Period	23/06/19 → 26/06/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Funding

This research is supported by the project (118E807) of Scientific and Technological Research Council of Turkey (TUBITAK). All of these supports are appreciated.

Funders	Funder number
TUBITAK
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Keywords

Footprint of Uncertainty
Fuzzy Mapping
Rational Polynomial Functions
Type-2 Fuzzy Logic Systems

Access to Document

10.1109/FUZZ-IEEE.2019.8858980

Cite this

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title = "A New Insight on the Mappings of Type-2 Fuzzy Logic Systems",

abstract = "In this paper, we provide a new insight on the mappings of Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) in comparison to its Type-1 (T1) counterparts. For the sake of simplicity, we focus on Single input IT2 (SIT2) FLSs that employ the Karnik Mendel (KM) or the Nie-Tan (NT) Centre of Sets Calculation Method (CSCM). Through theoretical investigations, it is shown that there does exist an equivalent SIT2-FLS representation with a Single input T1 (ST1) FLS that uses Rational Polynomial Functions (RBFs) in their rule consequents. It is concluded that SIT2-FLSs cannot be implemented with traditional ST1-FLSs. It is also revealed that the extra degree of freedom provided by IT2 fuzzy sets and CSCM results with RBFs that can generate much more complex mapping when compared to its T1 counterparts. It is also proven that SIT2-FLSs can be seen as adaptive ST1-FLSs that are tuned via a collection of ST1-FLSs. Thus, SIT2-FLSs have adaptive feature property that does not exists in ST1-FLSs. It is also shown that the SIT2-FLS employing the KM is more complex but also capable to accommodate a much wider range of mappings when compared its NT counterpart.",

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Kumbasar, T 2019, A New Insight on the Mappings of Type-2 Fuzzy Logic Systems. in 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019., 8858980, IEEE International Conference on Fuzzy Systems, vol. 2019-June, Institute of Electrical and Electronics Engineers Inc., 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019, New Orleans, United States, 23/06/19. https://doi.org/10.1109/FUZZ-IEEE.2019.8858980

A New Insight on the Mappings of Type-2 Fuzzy Logic Systems. / Kumbasar, Tufan.
2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8858980 (IEEE International Conference on Fuzzy Systems; Vol. 2019-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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A New Insight on the Mappings of Type-2 Fuzzy Logic Systems

Abstract

Publication series

Conference

Bibliographical note

Funding

Keywords

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