Uncertainty Avoider Interval Type II Defuzzification Method

Mathematical Problems in Engineering ◽

10.1155/2020/5812163 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Sadegh Aminifar

Keyword(s):

Fuzzy System ◽

Uncertainty Avoidance ◽

System Response ◽

Type Reduction ◽

Meaningful Relationship ◽

System Output ◽

Computational Bottleneck ◽

Interval Type

One of the IT2FS (interval type-2 fuzzy system) defuzzification methods uses the iterative KM algorithm. Because of the iterative nature of KM-type reduction, it may be a computational bottleneck for the real-time applications of IT2FSs. There are several other interval type-2 defuzzification methods suffering from lack of meaningful relationship between membership function uncertainties and changing of system output due to lack of clearly defined variables related to uncertainty in their methods. In this paper, a new approach for IT2FS defuzzification is presented by reconfiguring interval type-2 fuzzy sets and how uncertainties are present in them. This closed-formula method provides meaningful relation between the presence of uncertainty and its effect on system output. This study investigates uncertainty avoidance that the output of IT2FS obtained by centroid or bisection methods in comparison with type-1 fuzzy system (T1FLS) moves to points with less uncertainty. Uncertainty can enter into T1FSs and affect system response. Finally, for proving the affectivity of the proposed defuzzification method and uncertainty avoidance, several investigations are done and a prototype two-input one-output IT2FS MATLAB code is enclosed.

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Adaptive Backstepping Fuzzy Control Based on Type-2 Fuzzy System

Journal of Applied Mathematics ◽

10.1155/2012/658424 ◽

2012 ◽

Vol 2012 ◽

pp. 1-27 ◽

Cited By ~ 4

Author(s):

Ll Yi-Min ◽

Yue Yang ◽

Li Li

Keyword(s):

Fuzzy Control ◽

Fuzzy System ◽

External Disturbance ◽

Approximation Error ◽

Adaptive Backstepping ◽

Control Approach ◽

Type Reduction ◽

Adaptive Laws

A novel indirect adaptive backstepping control approach based on type-2 fuzzy system is developed for a class of nonlinear systems. This approach adopts type-2 fuzzy system instead of type-1 fuzzy system to approximate the unknown functions. With type-reduction, the type-2 fuzzy system is replaced by the average of two type-1 fuzzy systems. Ultimately, the adaptive laws, by means of backstepping design technique, will be developed to adjust the parameters to attenuate the approximation error and external disturbance. According to stability theorem, it is proved that the proposed Type-2 Adaptive Backstepping Fuzzy Control (T2ABFC) approach can guarantee global stability of closed-loop system and ensure all the signals bounded. Compared with existing Type-1 Adaptive Backstepping Fuzzy Control (T1ABFC), as the advantages of handling numerical and linguistic uncertainties, T2ABFC has the potential to produce better performances in many respects, such as stability and resistance to disturbances. Finally, a biological simulation example is provided to illustrate the feasibility of control scheme proposed in this paper.

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Uncertainty in Interval Type-2 Fuzzy Systems

Mathematical Problems in Engineering ◽

10.1155/2013/452780 ◽

2013 ◽

Vol 2013 ◽

pp. 1-16 ◽

Cited By ~ 3

Author(s):

Sadegh Aminifar ◽

Arjuna Marzuki

Keyword(s):

Fuzzy Systems ◽

System Response ◽

Membership Functions ◽

Degree Reduction ◽

Word Meanings ◽

Lower Complexity ◽

Interval Type

This paper studies uncertainty and its effect on system response displacement. The paper also describes how IT2MFs (interval type-2 membership functions) differentiate from T1MFs (type-1 membership functions) by adding uncertainty. The effect of uncertainty is modeled clearly by introducing a technique that describes how uncertainty causes membership degree reduction and changing the fuzzy word meanings in fuzzy logic controllers (FLCs). Several criteria are discussed for the measurement of the imbalance rate of internal uncertainty and its effect on system behavior. Uncertainty removal is introduced to observe the effect of uncertainty on the output. The theorem of uncertainty avoidance is presented for describing the role of uncertainty in interval type-2 fuzzy systems (IT2FSs). Another objective of this paper is to derive a novel uncertainty measure for IT2MFs with lower complexity and clearer presentation. Finally, for proving the affectivity of novel interpretation of uncertainty in IT2FSs, several investigations are done.

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Interpolation functions of interval Type-2 fuzzy systems

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210435 ◽

2021 ◽

pp. 1-17

Author(s):

Shan Zhao ◽

Zhao Li

Keyword(s):

Fuzzy System ◽

Fuzzy Systems ◽

Classical Type ◽

Data Sets ◽

Single Output ◽

Type Reduction ◽

Single Input ◽

Interval Type ◽

Interpolation Functions

The interpolation functions of interval type-2 fuzzy systems and their universal approximation are investigated in this paper. Two types of fuzzification methods are designed to construct the antecedents and consequents of the type-2 inference rules. Then the properties of the fuzzy operator and the type-reduction algorithm are used to integrate all parts of the fuzzy system. Interpolation functions of interval type-2 fuzzy systems, which are proved to be universal approximators, are obtained based on three models, namely single input and single output, double inputs and single output, and multiple inputs and single output. The proposed approach is applied to approximate experiments of dynamic systems so as to evaluate the system performance. The system parameters are optimized by the QPSO algorithm. Experimental results for several data sets are given to show the approximation performances of the proposed interpolation functions are better than those of the interpolation function of the classical type-1 fuzzy system.

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Artificial potential field neuro-fuzzy controller for autonomous navigation of mobile robots

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651820974831 ◽

2020 ◽

pp. 095965182097483

Author(s):

Mahamat Loutfi Imrane ◽

Achille Melingui ◽

Joseph Jean Baptiste Mvogo Ahanda ◽

Fredéric Biya Motto ◽

Rochdi Merzouki

Keyword(s):

Neural Networks ◽

Fuzzy Logic ◽

Mobile Robots ◽

Potential Field ◽

Autonomous Navigation ◽

Fuzzy Logic Controller ◽

Artificial Potential Field ◽

Type Reduction ◽

Interval Type

Some autonomous navigation methods, when implemented alone, can lead to poor performance, whereas their combinations, when well thought out, can yield exceptional performances. We have demonstrated this by combining the artificial potential field and fuzzy logic methods in the framework of mobile robots’ autonomous navigation. In this article, we investigate a possible combination of three methods widely used in the autonomous navigation of mobile robots, and whose individual implementation still does not yield the expected performances. These are as follows: the artificial potential field, which is quick and easy to implement but faces local minima and robustness problems. Fuzzy logic is robust but computationally intensive. Finally, neural networks have an exceptional generalization capacity, but face data collection problems for the learning base and robustness. This article aims to exploit the advantages offered by each of these approaches to design a robust, intelligent, and computationally efficient controller. The combination of the artificial potential field and interval type-2 fuzzy logic resulted in an interval type-2 fuzzy logic controller whose advantage over the classical interval type-2 fuzzy logic controller was the small size of the rule base. However, it kept all the classical interval type-2 fuzzy logic controller characteristics, with the major disadvantage that type-reduction remains the main cause of high computation time. In this article, the type-reduction process is replaced with two layers of neural networks. The resulting controller is an interval type-2 fuzzy neural network controller with the artificial potential field controller’s outputs as auxiliary inputs. The results obtained by performing a series of experiments on a mobile platform demonstrate the proposed navigation system’s efficiency.

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An interval type-2 hesitant fuzzy best-worst method

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202801 ◽

2021 ◽

pp. 1-28

Author(s):

Ashraf Norouzi ◽

Hossein Razavi hajiagha

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Group Decision Making ◽

Group Decision ◽

Fuzzy Ahp ◽

Uncertain Data ◽

Interval Type ◽

Best Worst Method

Multi criteria decision-making problems are usually encounter implicit, vague and uncertain data. Interval type-2 fuzzy sets (IT2FS) are widely used to develop various MCDM techniques especially for cases with uncertain linguistic approximation. However, there are few researches that extend IT2FS-based MCDM techniques into qualitative and group decision-making environment. The present study aims to adopt a combination of hesitant and interval type-2 fuzzy sets to develop an extension of Best-Worst method (BWM). The proposed approach provides a flexible and convenient way to depict the experts’ hesitant opinions especially in group decision-making context through a straightforward procedure. The proposed approach is called IT2HF-BWM. Some numerical case studies from literature have been used to provide illustrations about the feasibility and effectiveness of our proposed approach. Besides, a comparative analysis with an interval type-2 fuzzy AHP is carried out to evaluate the results of our proposed approach. In each case, the consistency ratio was calculated to determine the reliability of results. The findings imply that the proposed approach not only provides acceptable results but also outperforms the traditional BWM and its type-1 fuzzy extension.

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