Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Nazanin Sahab, Hani Hagras


Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.


Type-2 Fuzzy logic, non-singleton Fuzzy Logic Systems, interval type-2 fuzzy logic systems, Type-2 non-singleton type-2 FLS

Full Text:



L. A. Zadeh, Fuzzy Sets, Information and Control, 8, 338-353, 1965.

L. A. Zadeh, The Concept of a Linguistic Variable and its Application to Approximate Reasoning-I, Information Science 8, 199-249, 1975.

L. A. Zadeh, Outline of a New Approach to the Analysis of Complex Systems and Decision Processes, IEEE Transactions on Systems, Man, and Cybernetics, pp.28-44, 1973.

E. H. Mamdani, S. Assilian, An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller, International Journal of Man-Machine Studies (1975), Vol. 7, No. 1, pp.1-13, 1975.

G. Feng, A Survey on Analysis and Design of Model-Based Fuzzy Control Systems, IEEE Transactions on Fuzzy Systems, Vol. 14, No. 5, pp.676-697, 2006.

P. P. Bonissone, V. Badami, K. H. Chiang, P. S. Khedkar, K. W. Marcelle, M. J. Schutten, Industrial Applications of Fuzzy Logic at General Electric, Proceedings of IEEE, Vol. 83, No. 3, pp.450-465, 1995.

B. Choi, S. Han, S. Hong, Refrigerator Temperature Control Using Fuzzy Logic and Neural Network, IEEE International Symposium on Industrial Electronics, Vol. 1, pp.186-191, 1998. products_id=5847

R. John, S. Coupland, Type-2 Fuzzy Logic: A Historical View, IEEE Computational Intelligence Magazine, Vol. 2, No. 1, pp.57-62, 2007.

D. Wu, W. W. Tan, Genetic Learning and Performance Evaluation of Interval Type-2 Fuzzy Logic Controllers, Engineering Applications of Artificial Intelligence, Vol. 19 No. 8, pp. 829- 841, 2006.

N. Sahab, H. Hagras, An Adaptive Type-2 Input Based Non-Singleton Type-2 Fuzzy Logic System for Real World Applications, IEEE International conference on Fuzzy Systems 2011.

A. Perez-Neira, J. Sueiro, and J. Roca and M. Lagunas, A Dynamic Non-singleton Fuzzy Logic System for DS/CDMA Communications, IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 1494-1499, 1998.

M. Benedetti, A. Casagranda, and M. Donelli, and A. Massa, An Adaptive Multiscaling Imaging Technique Based on a Fuzzy-logic Strategy for Dealing with the Uncertainty of Noisy Scattering Data, IEEE Transactions on Antennas and Propagation, Vol. 55, No. 11, pp. 3265-3278, 2007.

C. K. Makropoulos and D. Butler, Spatial decisions under uncertainty: fuzzy inference in urban water management, Journal of Hydroinformatics, IWA publishing, pp. 3-18, 2004.

C. Quek and R. Zhou, Structure and learning algorithms of a nonsingleton input fuzzy neural network based on the approximate analogical reasoning schema, International Journal on Information Science and Engineering Science (Fuzzy Sets and Systems), Elsevier, vol.157, no. 13, pp. 1814-1831, 2006.

E. Cavallaro, S. Micera, and P. Dario, and W. Jensen, and T. Sinkjaer,On the Intersubject Generalization Ability in Extracting Kinematic Information from Afferent Nervous Signals, IEEE Transactions on Biomedical Engineering, Vol.50, No. 9, pp. 1063-1073, 2003.

T. Chua and W. Tan, Non-singleton genetic fuzzy logic system for arrhythmias classification, Engineering Applications of Artificial Intelligence, Elsevier, Vol. 24, No. 2, Pages 251-259, 2011.

G. M. Mendez, L. L. Lezma, R. Colas, G. M. Perez, J. R. Cuellar, J. J. Lopez, Application of Interval Type-2 Fuzzy Logic Systems for Control of Coiling Entry Temperature in Hot Strip Mill, International conference on Hybrid Artificial intelligent Systems, pp.352-359, Springer- Verlag Berlin 2009.

G. M. Mendez, M. A. Hernandez, Interval Type-1 Non-Singleton Type-2 TSK Fuzzy Logic Systems Using the Hybrid Training Method RLS-BP, IEEE Symposium on Foundations of computational Intelligence, pp.370-374, 2007.

G. M. Mendez, A. Hernandez, Hybrid IT2 NSFLS-1 Used to Predict the Uncertain MXNUSD Exchange Rate, Springer-Verlag Berlin Heidelberg 2008, pp. 575-582, 2008.

G. M .Mendez, A. Hernandez, A. Cavazos, M. T. M. Jimenez, Type-1 Non-singleton Type- 2 Takagi-Sugeno-Kang Fuzzy Logic Systems Using the Hybrid Mechanism Composed by a Kalman Type Filter and Back Propagation Methods, Springer-Verlag Berlin Heidelberg 2010, pp.429-437, 2010.

G. M. Mendez, L. A. Leduc, First-Order Interval Type-1 Non-singleton Type-2 TSK Fuzzy Logic Systems, Springer-Verlag Berlin Heidelberg ,pp.81-89, 2006.

G. M. Mendez, Interval Type-1 Non-singleton Type-2 Fuzzy Logic Systems are Type-2 Adaptive Neuro-Fuzzy Inference Systems, International Journal of Reasoning-based Intelligent Systems, Vol. 2, No. 2, pp.95-99, 2010.

G. M. Mendez, I. L. Juarez, L. A. Leduc, R. Soto, A. Cavazos, Temperature Prediction in Hot Strip Mill Bars Using a Hybrid Type-2 Fuzzy algorithm, International Journal of Simulation Systems, Science & Technology, pp.33-43, 2005.

G. M. Mendez, M. A. Hernandez, Hybrid Learning for Interval Type-2 Fuzzy Logic Systems Based on Orthogonal Least-squares and Back-propagation Methods, International Journal on Information Science, Vol. 179, No. 13, pp.2146-2157, 2009.

G. Mendez, A. Hernandez, Hybrid Learning of Interval Type-2 Fuzzy Systems Based on Orthogonal Least Squared and Back Propagation for Manufacturing Applications, Journal of Automation, Mobile Robotics & Intelligent Systems, pp.23-32, 2008.

H. Wu, J. M. Mendel, "Classification of battlefield ground vehicles using acoustic features and fuzzy logic rule-based classifiers", IEEE transactions on fuzzy systems, Vol. 15, No. 1, pp.56-72, 2007.

G. Mendez, M. Hernandez, IT2 TSK NSFLS2 ANFIS, Ninth Mexican International Conference on Artificial Intelligence, IEEE Computer Society, pp.89-93, 2010.

G. Mendez, M. Hernandez, Interval Type-2 Non-singleton Type-2 Takagi-Sugeno-Kang Fuzzy Logic Systems Using the Hybrid Learning Mechanism Recursive-Least-Square and Back-Propagation Methods, IEEE International Conference on Control, Automation, Robotics and Vision, Singapore, pp.710-714, 2010.

P. Torres, D. Saez, Type-2 Fuzzy Logic Identification Applied to the Modeling of a Robot Hand, IEEE International conference on Fuzzy Systems, pp.854-861, 2008.

J. M. Mendel, Uncertain Rule-based Fuzzy Logic Systems, introduction and new direction, Prentice Hall PTR Upper Saddle river, NJ, 2001.

Q. Liang, J. M. Mendel, Interval Type-2 Fuzzy Logic Systems: Theory and Design, IEEE Transactions on Fuzzy Systems, Vol.8, No.5, pp.535-550, 2000.

G. C. Mouzouris, J. M. Mendel, Nonsingleton Fuzzy Logic Systems: Theory and Application, IEEE Transactions on Fuzzy Systems, Vol.5, No.1, pp.56-71, 1997.

J. L. S. Neto, L. H. Hoang, G. C. Mouzouris, J. M. Mendel, Comments on "Nonsingleton fuzzy logic systems: theory and applications" and Reply, IEEE Transactions on Fuzzy Systems, Vol.6, No.2, pp.325-326, 1998.

S. Coupland, R. John, Geometric Interval Type-2 Fuzzy Systems, Proceedings of the joint 4th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2005) and the 11th LFA (joint EUSFLAT-LFA 2005), pp.449-454, 2005.

H. Hagras, Type-2 FLCs: A New Generation of Fuzzy Controllers, IEEE Computational Intelligence Magazine, Vol. 2, No. 1, pp.30-43, 2007.

J. M. Mendel, Type-2 Fuzzy Sets: Some Questions and Answers, Feature article in IEEE Neural Network Society, pp.10-13, 2003.

J. M. Mendel, Advances in Type-2 Fuzzy Sets and Systems, Information Sciences 177 (2007) 84-110, 2006.

N. N. Karnik, J. M. Mendel, Q. Liang, Type-2 Fuzzy Logic Systems, IEEE Transactions on Fuzzy Systems, Vol. 7, No. 6, pp. 643-658, 1999.

Q. Liang, N. N. Karnik, J. M. Mendel, Connection Admission Control in ATM Networks Using Survey-Based Type-2 Fuzzy Logic Systems, IEEE Transactions on Systems, Man, and Cybernetics- Part-C: Applications and Reviews, Vol. 30, No. 3, pp.329-339, 2000.

J. M. Mendel, R. B. John, Type-2 Fuzzy Sets Made Simple, IEEE Transactions on Fuzzy Systems, Vol. 10, No. 2, pp.117-127, 2002.

J. Mendel, H. Wu, Uncertainty Versus Choice in Rule-based Fuzzy Logic Systems , IEEE International Conference on Fuzzy Systems, pp.1336-1342, 2002.

J. M. Mendel, Type-2 Fuzzy Sets and Systems: How to Learn About Them, IEEE SMC eNewsletter, 2009.

E. A. Jammeh, M. Fleury, C.Wagner, H. Hagras, M. Ghanbari, Type-2 Fuzzy Logic Congestion Control for Video Streaming Across IP Networks, IEEE Transactions on Fuzzy Systems, Vol. 17, No. 5, pp.1123-1142, 2009.

S. Barkati, E. M. Berkouk , M. S. Boucherit, Application of Type-2 Fuzzy Logic Controller to An Induction Motor Drive with Seven-level Diode-clamped Inverter and Controlled Infeed, Electrical Engineering Journal- Spring Berlin, Vol.90, No. 5, pp.347-359, 2008.

F. J. Lin, P. H. Chou, Adaptive Control of Two-axis Motion Control System Using Interval Type-2 Fuzzy Neural Network, IEEE Transactions on Industrial Electronics, Vol. 56, No. 1, pp.178-193, 2009.

N. Sahab, H. Hagras, A Type-2 Nonsingleton Type-2 Fuzzy Logic System to Handle Linguistic and Numerical Uncertainties in RealWorld Environments, IEEE International Symposium on Advances in Type-2 Fuzzy Logic Systems 2011.

A. Ferreoro, S. Salicone, Fully comprehensive mathematical approach to the expression of uncertainty in measurement, IEEE Transactions on Instrumentation and Measurement, Vol. 55, No. 3, pp.706-712, 2006.

N. Sahab, H. Hagras, A Hybrid Approach to Modeling Input Variables in Non-Singleton Type-2 Fuzzy Logic Systems, The 10th Annual UK Workshop in Computational Intelligence (UKCI 2010), pp. 1-6, 2010.

F. Liu, J. M. Mendel, An Interval Approach to Fuzzistics for Interval Type-2 Fuzzy Sets, IEEE International Conference on Fuzzy Systems, pp.1-6, 2007.

J. Lamancusa (2000), Outdoor Sound Propagation, Noise Control, ME 458: Engineering Noise Control, Penn State University, pp.10-19, 2009.


Copyright (c) 2017 Nazanin Sahab, Hani Hagras

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2016: IF=1.374. .

IJCCC is indexed in Scopus from 2008 (CiteScore 2017 = 1.04; SNIP2017 = 0.616, SJR2017 =0.326):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2017 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.29 (Q3). Scopus: CiteScore2017=1.04 (Q2); Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.