Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Zakaria, Rozaimi; Wahab, Abd. Fatah; Ismail, Isfarita; Zulkifly, Mohammad Izat Emir

doi:10.3390/math9091054

Cited by 12 publications

(5 citation statements)

References 26 publications

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“…The most recent studies on the type-reduction of interval type-2 fuzzy set have shown that the continuous version of NT (CNT) algorithms is an accurate method for defuzzifing [34]. Intuitively, we can feel that if the sampling size approaches infinity, random sampling will become an accurate TR method.…”

Section: Nt and Cntmentioning

confidence: 99%

Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System

Qin

Zhang²,

Zhao³

et al. 2022

Processes

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This paper proposes a dynamic high-type control (DHTC) method based on an interval type-2 fuzzy logic controller (IT2FLC), which is used in the photoelectric tracking system to improve the steady-state accuracy and response speed. Adding integrators to the traditional multi-loop feedback control loop can increase the system type, thereby speeding up the response speed and improving the steady-state accuracy, but there is a risk of integral saturation. Switching the type dynamically according to the system state can avoid integral saturation while retaining the advantages of the high-type. Fuzzy logic control (FLC) can dynamically change the output value according to the input change and has the advantages of fast response speed and strong ability to handle uncertainties. Therefore, in this paper, the FLC is introduced into the high-type control system, and the output of the FLC is used as the gain of the integrator to control the on-off to achieve the goal of dynamic switching type, which is successfully verified in the experiment. IT2FLC introduces a three-dimensional membership function, which further improves the FLC’s ability to handle uncertainties. From the experimental results, compared with T1FLC, IT2FLC’s ability to handle uncertainties is significantly improved. In addition, in order to speed up the calculation speed of IT2FLC, this paper proposes an improved type-reduction algorithm, which is called weighted-trapezoidal Nie-Tan (WTNT). Compared with the traditional type-reduction algorithm, WTNT has faster calculation speed and better steady-state accuracy, and has been successfully applied to real-time control systems, which has good engineering application value. Finally, in order to reduce the interference of human factors and improve the automation level of the system, a multi-population genetic algorithm (MPGA) is used to iteratively optimize the parameters of the FLC, which improves the output accuracy. On the experimental platform of the flexible fast steering mirror (FFSM), the control effects of the traditional controller, T1FLC and IT2FLC are compared, which proves that the IT2FLC-DHTC system has a faster response performance, higher steady-state accuracy, and stronger ability to handle uncertainties.

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Section: Nt and Cntmentioning

confidence: 99%

Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System

Qin

Zhang²,

Zhao³

et al. 2022

Processes

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“…Cuong et al [5] explained on several computations of type-2 intuitionistic fuzzy sets (T-2IFS) and T-2IFS can deal with complex uncertainties similar to T-2FS since they are considering the non-membership function [3]. [22,25,26] or surface such as [24,21]. The implementation of the concept of fuzzy number or its extension to define the data is necessary to tackle the core issue and followed by fuzzification, type-reduction (if necessary) and defuzzification before they are blended with the curve or surface function in order to construct the model.…”

Section: Introductionmentioning

confidence: 99%

Type-2 Intuitionistic Interpolation Cubic Fuzzy Bézier Curve Modeling using Shoreline Data

Ahmad Azmi,

Zakaria,

Ismail

2023

Mal. J. Fund. Appl. Sci.

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The notion of fuzzy sets is fast becoming a key instrument in defining the uncertainty data and has increasingly been recognised by practitioners and researchers across different disciplines in recent decades. The uncertainty data cannot be modeled directly and this causes hindrance in obtaining accurate information for analysis or predictions. Hence, this paper contributes to another approach in which an application of type-2 intuitionistic fuzzy set (T-2IFS) in geometric modeling onto complex uncertainty data where the data are defined using the type-2 fuzzy concept. T-2IFS is the generalized forms of fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and interval-valued intuitionistic fuzzy sets. Based on the concept of T2IFS, type-2 intuitionistic fuzzy point (T-2IFP) is defined in order to generate a type-2 intuitionistic fuzzy control point (T-2IFCP). Following, the T-2IFCP will be blended with the Bernstein blending function through the interpolation method, resulting to a type-2 intuitionistic interpolation cubic fuzzy Bézier curve. Shoreline data is used as the data and further verifies that the model can be conceivably accepted. In conclusion, the proposed methods are reliable and can be expanded to many other areas.

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“…The unpredictability of the data was caused by human and machine error, environmental defects, environmental problems, and other factors. Modeling cannot directly use this data on uncertainty [5]. In 1965, Zadeh used fuzzy set theory for the first time to describe problems with unclear data.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Intuitionistic Alpha Cut of B-Spline Curve Interpolation Modeling for Shoreline Island Data

Jifrin,

Zakaria,

Ismail

2023

Mal. J. Fund. Appl. Sci.

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Traditional approaches are unable to handle the uncertainty data issue, which leads to inaccurate data analysis and prediction. Data with uncertainty are frequently collected during the data collection phase but cannot be directly used to create geometric models. Therefore, using intuitionistic alpha cuts for the uncertainty data, this paper discusses B-Spline curve interpolation modeling. To resolve the uncertain data and produce the mathematical model, fuzzy set theory, intuitionistic fuzzy sets, and geometry modeling are combined. Three main procedures are used in detail, the first of which is the application of fuzzy set theory to defined uncertainty data, followed by the use of an intuitionistic fuzzy set to take into account the membership, non-membership, and indeterminacy values of the alpha, and finally the fuzzification and defuzzification procedures. The B-spline curve interpolation function is used in geometric modeling to create mathematical geometry in the form of curves. As a result, several numerical examples are provided, along with their algorithms for producing the desired curve.

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Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Cited by 12 publications

References 26 publications

Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System

Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System

Type-2 Intuitionistic Interpolation Cubic Fuzzy Bézier Curve Modeling using Shoreline Data

Fuzzy Intuitionistic Alpha Cut of B-Spline Curve Interpolation Modeling for Shoreline Island Data

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