Abstract
We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi-Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.
| Original language | English |
|---|---|
| Article number | 8848600 |
| Pages (from-to) | 2665-2672 |
| Number of pages | 8 |
| Journal | IEEE Transactions on Fuzzy Systems |
| Volume | 28 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - Oct 2020 |
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Santoso, F., Garratt, M. A., & Anavatti, S. G. (2020). T2-ETS-IE: A Type-2 Evolutionary Takagi-Sugeno Fuzzy Inference System with the Information Entropy-Based Pruning Technique. IEEE Transactions on Fuzzy Systems, 28(10), 2665-2672. [8848600]. https://doi.org/10.1109/TFUZZ.2019.2943813
Santoso, Fendy ; Garratt, Matthew A. ; Anavatti, Sreenatha G. / T2-ETS-IE : A Type-2 Evolutionary Takagi-Sugeno Fuzzy Inference System with the Information Entropy-Based Pruning Technique. In: IEEE Transactions on Fuzzy Systems. 2020 ; Vol. 28, No. 10. pp. 2665-2672.
@article{20a8d32726bd4fae9301e6b1ddaf37ce,
title = "T2-ETS-IE: A Type-2 Evolutionary Takagi-Sugeno Fuzzy Inference System with the Information Entropy-Based Pruning Technique",
abstract = "We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi-Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.",
keywords = "Evolutionary Takagi-Sugeno (ETS) fuzzy system, information entropy, learning-from-scratch, Type-2 fuzzy system",
author = "Fendy Santoso and Garratt, {Matthew A.} and Anavatti, {Sreenatha G.}",
note = "Funding Information: Manuscript received October 21, 2018; revised March 26, 2019 and July 12, 2019; accepted August 29, 2019. Date of publication September 25, 2019; date of current version October 6, 2020. This work was supported by an internal research funding from the University of New South Wales, Canberra, Australia. (Corresponding author: Fendy Santoso.) The authors are with the School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT 2600, Australia (e-mail: fendy.santoso@gmail.com). Publisher Copyright: {\textcopyright} 1993-2012 IEEE.",
year = "2020",
month = oct,
doi = "10.1109/TFUZZ.2019.2943813",
language = "English",
volume = "28",
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Santoso, F, Garratt, MA & Anavatti, SG 2020, 'T2-ETS-IE: A Type-2 Evolutionary Takagi-Sugeno Fuzzy Inference System with the Information Entropy-Based Pruning Technique', IEEE Transactions on Fuzzy Systems, vol. 28, no. 10, 8848600, pp. 2665-2672. https://doi.org/10.1109/TFUZZ.2019.2943813
T2-ETS-IE: A Type-2 Evolutionary Takagi-Sugeno Fuzzy Inference System with the Information Entropy-Based Pruning Technique. / Santoso, Fendy; Garratt, Matthew A.; Anavatti, Sreenatha G.
In: IEEE Transactions on Fuzzy Systems, Vol. 28, No. 10, 8848600, 10.2020, p. 2665-2672.
Research output: Contribution to journal › Article › peer-review
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AU - Anavatti, Sreenatha G.
N1 - Funding Information:Manuscript received October 21, 2018; revised March 26, 2019 and July 12, 2019; accepted August 29, 2019. Date of publication September 25, 2019; date of current version October 6, 2020. This work was supported by an internal research funding from the University of New South Wales, Canberra, Australia. (Corresponding author: Fendy Santoso.) The authors are with the School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT 2600, Australia (e-mail: fendy.santoso@gmail.com).Publisher Copyright:© 1993-2012 IEEE.
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N2 - We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi-Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.
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Santoso F, Garratt MA, Anavatti SG. T2-ETS-IE: A Type-2 Evolutionary Takagi-Sugeno Fuzzy Inference System with the Information Entropy-Based Pruning Technique. IEEE Transactions on Fuzzy Systems. 2020 Oct;28(10):2665-2672. 8848600. doi: 10.1109/TFUZZ.2019.2943813
FAQs
What is Takagi Sugeno fuzzy inference method? ›
Sugeno method develops a systematic approach to generate fuzzy rules from a given input-output data set. It changes the consequent (then part) of Mamdani rule with a function (Equation) of the input variables.
What are the two types of fuzzy inference system? ›Two main types of fuzzy inference systems can be implemented: Mamdani-type (1977) and Sugeno-type (1985). These two types of inference systems vary somewhat in the way outputs are determined.
What is the difference between Mamdani and Sugeno method? ›The most fundamental difference between Mamdani type FIS and Sugeno type FIS is the way the crisp output is generated from the fuzzy inputs. While Mamdani FIS uses the technique of defuzzification of a fuzzy output, Sugeno FIS uses weighted average to compute the crisp output.
Which system does Sugeno FIS use? ›Sugeno systems always use the "prod" implication method, which scales the consequent membership function by the antecedent result value. For more information on implication and the fuzzy inference process, see Fuzzy Inference Process.
What is sugeno fuzzy logic? ›A typical rule in a Sugeno fuzzy model has the form: If Input 1 = x and Input 2 = y,then Output is z=ax+by+c. For a zero-order Sugeno model, the output level z is a constant (a=b =0). The output level zi of each rule is weighted by the firing strength w of the. rule.
What is the difference between fuzzy type1 and type 2? ›A type-1 fuzzy set is characterized by a two-dimensional MF, whereas a type-2 fuzzy set is characterized by a three-dimensional MF. As an example, suppose that the variable of interest is eye contact, which we denote as x. Let's put eye contact on a scale of values 0–10.
What are the advantages of type-2 fuzzy logic? ›Type-2 fuzzy logic systems (T2FLSs) offer opportunity to model levels of uncertainty which traditional fuzzy logic type1 struggles. This extra dimension gives more degrees of freedom for better representation of uncertainty compared to type-1 fuzzy sets.
Why type-2 fuzzy systems are needed? ›Type-2 fuzzy sets are finding very wide applicability in rule-based fuzzy logic systems (FLSs) because they let uncertainties be modeled by them whereas such uncertainties cannot be modeled by type-1 fuzzy sets.
What is the difference between Takagi Sugeno fuzzy and Mamdani? ›The main difference between them is that the consequence parts of Mamdani fuzzy model are fuzzy sets while those of the Takagi–Sugeno fuzzy model are linear functions of input variables !!! - Output membership function is attendant. - Mamdani inference system is well suited to human input .
What are the advantages of Sugeno? ›| Fuzzy Inference System | Advantages |
|---|---|
| Sugeno | ● Computationally efficient ● Functions well with linear techniques, like PID control ● Functions with optimization and adaptive techniques ● Guarantees output surface continuity ● Well-suited to mathematical analysis |
What is sugeno model? ›
The Sugeno Fuzzy model (also known as the TSK fuzzy model) was proposed by Takagi, Sugeno, and Kang in an effort to develop a systematic approach to generating fuzzy rules from a given input-output dataset.
What is fuzzy logic rule? ›What Does Fuzzy Rule Mean? A fuzzy rule is a conditional "if-then" statement thusly stated: "If 'x' equals A. then 'y' equals B." It's the rule which governs the operation of fuzzy logic controllers.
Where are fuzzy expert systems used? ›The fuzzy expert system is a form of problem solving used by a computer system, often used in the creation of artificial intelligence.
What is meant by fuzzy logic? ›Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based. The idea of fuzzy logic was first advanced by Lotfi Zadeh of the University of California at Berkeley in the 1960s.
What is the real life application of fuzzy inference system? ›Fuzzy logic has been used in numerous applications such as facial pattern recognition, air conditioners, washing machines, vacuum cleaners, antiskid braking systems, transmission systems, control of subway systems and unmanned helicopters, knowledge-based systems for multiobjective optimization of power systems, ...
What are the 4 parts of fuzzy logic? ›A typical fuzzy system can be split into four main parts, namely a fuzzifier, a knowledge base, an inference engine and a defuzzifier; The fuzzifier maps a real crisp input to a fuzzy function, therefore determining the 'degree of membership' of the input to a vague concept.
What is an example of a fuzzy logic worked? ›- Control of automatic exposure in video cameras.
- Humidity in a clean room.
- Air conditioning systems.
- Washing machine timing.
- Microwave ovens.
- Vacuum cleaners.
Methods of FIS
There are two different types of fuzzy inference system which have a different consequent of the fuzzy rule. These are the Mamdani fuzzy inference system and the Takagi-Sugeno Fuzzy Model or the TS Method.
Type-1 fuzzy sets
A type-1 fuzzy set can be represented as a type-2 fuzzy set. Its type-2 representation is: The value of 1 means that the secondary membership function has only one value in its domain, i.e. the primary membership at which the secondary grade is equal to 1.
If = ((1, 1, 1), (1, 1, 1), (1, 1, 1)) then is said to be a type-2 unit triangular fuzzy number. It is denoted by 1. A type-2 triangular fuzzy number is said to be a type-2 unit-equivalent triangular fuzzy number if Ř ( ) = 1. It is denoted by 1.
What can we do with type-2 fuzzy logic sets? ›
Abstract—Type-2 fuzzy sets let us model and minimize the ef- fects of uncertainties in rule-base fuzzy logic systems.
Is fuzzy logic easy or hard? ›Fuzzy logic is conceptually easy to understand. The mathematical concepts behind fuzzy reasoning are very simple. Fuzzy logic is a more intuitive approach without the far-reaching complexity. Fuzzy logic is flexible.
What is type-2 fuzzy logic? ›We can say that type-2 fuzzy logic is a generalization of conventional fuzzy logic (type-1) in the sense that uncertainty is not only limited to the linguistic variables but also is present in the definition of the membership functions.
Is fuzzy logic still useful? ›Fuzzy logic is widely used for commercial and practical purposes. It helps you to control machines and consumer products.
What are the advantages and disadvantages of fuzzy system? ›| Advantages | Disadvantages |
|---|---|
| It asks you to manage vulnerabilities in the design process | Occasionally, the fuzzy rationale is mistaken for likelihood hypothesis |
| Generally strong as no exact information sources required |
A Sugeno fuzzy inference system is suited to the task of smoothly interpolating the linear gains that would be applied across the input space; it is a natural and efficient gain scheduler. Similarly, a Sugeno system is suited for modeling nonlinear systems by interpolating between multiple linear models.
What is the advantage of fuzzy inference system? ›The benefits of using Fuzzy Logic systems are as follows: It is a robust system where no precise inputs are required. These systems are able to accommodate several types of inputs including vague, distorted or imprecise data. In case the feedback sensor stops working, you can reprogram it according to the situation.
What is the difference between fuzzy system and crisp system? ›A fuzzy set defines the degree to which anything is true. On the other hand, the Crisp set is also known as a classical set. The fuzzy set specifies a number between 0 and 1, which includes both 0 and 1. On the other hand, the crisp set specifies the value as either 0 or 1.
What is the difference between binary and fuzzy? ›In a binary system, a sample either belongs to a class or not (meaning that the degree of membership is either 1 or 0), whereas in the fuzzy system, a sample can belong to different classes with different degrees of membership (that all add up to 1).
What are the advantages of fuzzy logic in pattern recognition? ›Fuzzy logic helps in solving the situations in which we are uncertain like the situation of maybe yes or maybe not and combining it with pattern recognition helps us to recognise or organize the patterns in a certain manner.
Which method is also known as sugeno defuzzification? ›
Weighted average method is one of the simplest and widely used defuzzification technique. This method is also alternatively called ”Sugeno defuzzification” method.
What are the advantages of adaptive neuro fuzzy inference system? ›| Advantages | Disadvantages |
|---|---|
| Captures nonlinearity of a process | Selecting type and number of membership functions |
| Automatic adaptation capability | Location of a membership function |
| Rapid learning capacity | Curse of dimensionality |
| High generalization capability | Interpretability-accuracy trade-off |
In Sugeno, the output is a linear constant, while the Tsukamoto method produces a fuzzy set of output.
What are the different types of fuzzy models? ›Two types of rule-based fuzzy models are described: the linguistic (Mamdani) model and the Takagi–Sugeno model.
What is fuzzy logic for dummies? ›Fuzzy logic is an approach to variable processing that allows for multiple possible truth values to be processed through the same variable. Fuzzy logic attempts to solve problems with an open, imprecise spectrum of data and heuristics that makes it possible to obtain an array of accurate conclusions.
What are the three stages of fuzzy logic? ›1.9 Fuzzy Logic Controller as MPPT
FLC generally consists of three stages: fuzzification, aggregation, and defuzzification.
Fuzzy rule connectors
For example, IF temperature is hot AND humidity is high. THEN fan speed is fast. The degree of truth assigned to temperature is hot and to humidity is high.
In addition to rice cookers, devices like automatic washing machines, refrigerators, computers and even subway cars use fuzzy logic to function.
Does Google use fuzzy logic? ›A fuzzy matching search algorithm will be able to find relevant strings even if your original string contains typo errors and misspellings. Ever seen Google correcting you like this? That's Google using fuzzy search to match your misspelled query to the word with the correct spelling.
What is an example of a fuzzy reasoning? ›Propositions in Fuzzy Logic
For example, “Delhi is the capital of India”, this is a proposition where “Delhi” is the subject and “is the capital of India” is the predicate which shows the property of subject.
What is an example of fuzzy data? ›
Description. Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data.
What are the main differences between Mamdani and Takagi-Sugeno fuzzy inferences? ›The main difference between them is that the consequence parts of Mamdani fuzzy model are fuzzy sets while those of the Takagi–Sugeno fuzzy model are linear functions of input variables !!!
What is fuzzy based method? ›Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based. The idea of fuzzy logic was first advanced by Lotfi Zadeh of the University of California at Berkeley in the 1960s.
What is the method of fuzzy logic? ›Fuzzy logic is an approach to variable processing that allows for multiple possible truth values to be processed through the same variable. Fuzzy logic attempts to solve problems with an open, imprecise spectrum of data and heuristics that makes it possible to obtain an array of accurate conclusions.
What is the difference between a Type 1 fuzzy set and a Type 2 fuzzy set? ›A type-1 fuzzy set is characterized by a two-dimensional MF, whereas a type-2 fuzzy set is characterized by a three-dimensional MF. As an example, suppose that the variable of interest is eye contact, which we denote as x. Let's put eye contact on a scale of values 0–10.
What are some examples of fuzzy logic in the real world? ›- Altitude control of spacecraft.
- Satellite altitude control.
- Flow and mixture regulation in aircraft deicing vehicles.
The paradigm of fuzzy modelling entails development of relationships (dependencies) between the linguistic entities defined for system's variables. The key feature of the fuzzy models pertains to their significant flexibility so they could easily be modified to comply with the principle of incompatibility.