On Nie-Tan Operator and Type-Reduction of Interval Type-2 Fuzzy Sets

Li, Jiawei; John, Robert; Coupland, Simon; Kendall, Graham

doi:10.1109/tfuzz.2017.2666842

Cited by 68 publications

(57 citation statements)

References 23 publications

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“…Nie‐Tan operator had been considered as a first‐order Taylor series approximation to the KM algorithm, and its improved extension had been considered as a first‐order Taylor series approximation to the KM algorithm . Nie‐Tan type reduction method has good accuracy, and it satisfies the defuzzification properties required for discrete as well as continuous interval type‐2 fuzzy system . The fuzzy base for interpolation is calculated by using the Nie‐Tan method by the average of the upper and lower interval rules .…”

Section: Hybrid Interval Type‐2 Fuzzy Kalman Filtermentioning

confidence: 99%

“…A number of computationally efficient type reduction approaches have been proposed in literature . Here, a low computational cost Nie‐Tan method is used . The huge computational complexity of the type reduction algorithm is considered as the bottleneck for the type‐2 fuzzy systems.…”

Section: Computational Complexity Analysismentioning

confidence: 99%

“…Nie Tan method is computationally less complex than any numerical methods in defuzzification of continuous IT2 FSs. Nie‐Tan operator is reliable for concrete as well as continuous IT2 FSs and holds equivalence to exhaustive type‐reduction methods . Experimentally, it has been shown that the Greenfield‐Chiclana collapsing defuzzifier is the most accurate defuzzification method, but with no statistical evidence when compared with the Nie‐Tan method.…”

Section: Computational Complexity Analysismentioning

confidence: 99%

“…55 The fuzzy base for interpolation is calculated by using the Nie-Tan method by the average of the upper and lower interval rules. 55 The region between the lower MF and the upper MF is the footprint of uncertainty which leads to the unique fuzziness property of its MFs. An elaborate mathematical description of the algorithm in Figure 3 is discussed next.…”

Section: Hybrid Interval Type-2 Fuzzy Kalman Filtermentioning

confidence: 99%

“…59 Here, a low computational cost Nie-Tan method is used. 55 The huge computational complexity of the type reduction algorithm is considered as the bottleneck for the type-2 fuzzy systems. Hence, in the proposed method, low computational cost Nie-Tan type reduction method 55 is adopted.…”

Section: Computational Complexity Analysismentioning

confidence: 99%

See 4 more Smart Citations

Interval type‐2 fuzzy Kalman filter aided individual channel estimation in MIMO relay systems

Kaur

Khosla

Sarin

2018

Int J Communication

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Summary For a multiple input multiple output relay system, the overall system performance is dependent on the effectiveness of the channel estimation technique adopted. In real time, communicating nodes have Doppler offset influences associated with them owing to high mobility that largely affects the characteristics of underlying channels. Thus, for the complete characterisation of the channel under fast time varying fading conditions, the estimation of the Doppler offset influences along with the channel coefficients becomes inevitable. However, the combined estimation of the channel and the Doppler influences renders the overall estimation problem nonlinear. In literature, majority of the channel estimation methods assume that the Doppler offset influences are already known to the receiver node or nodes are assumed to be stationary. In this paper, a novel hybrid interval type‐2 fuzzy aided Kalman filter method is proposed for the nonlinear channel estimation problem in one‐way two‐hop multiple input multiple output relay system. This channel estimation issue is represented as a nonlinear state space model, and the proposed hybrid method that combines the merits offered by the interval type‐2 fuzzy interpolation and the Kalman filter approach is applied to address the issue. For type reduction, Nie‐Tan method is adopted which is a low computational load extension of the widely used Karnik‐Mendel approach. Furthermore, a computational complexity analysis has been performed. The proposed hybrid interval type‐2 fuzzy based Kalman filter approach shows good performance‐complexity trade off under fast time varying channel conditions for one‐way two‐hop multiple input multiple output relay system.

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Section: Hybrid Interval Type‐2 Fuzzy Kalman Filtermentioning

confidence: 99%

Section: Computational Complexity Analysismentioning

confidence: 99%

Section: Computational Complexity Analysismentioning

confidence: 99%

Section: Hybrid Interval Type-2 Fuzzy Kalman Filtermentioning

confidence: 99%

Section: Computational Complexity Analysismentioning

confidence: 99%

See 3 more Smart Citations

Interval type‐2 fuzzy Kalman filter aided individual channel estimation in MIMO relay systems

Kaur

Khosla

Sarin

2018

Int J Communication

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Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

Namadchian

Zare

2020

Asian Journal of Control

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The present paper aims to analyze the stability of dynamic Interval Type-2 fuzzy control systems (IT2 FCSs) with adjustable parameters by investigating the existence of limit cycles based on the describing function (DF) method. To simplify the stability analysis, the following structured procedure is described. First, to avoid complex computation, a simple architecture of the IT2 FCS using two embedded Type-1 fuzzy control systems (T1 FCSs) is proposed. Then, the DF of IT2 FCS is obtained based on the DFs of embedded T1FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stability regions. Moreover, particle swarm optimization (PSO) technique is utilized to minimize the limit cycle region. Other focus of this paper is on the stability margins analysis for robust design. For this purpose, a gain-phase margin tester is applied to determine the minimum Gain Margin (GM min ) and Phase Margin (PM min ) when limit cycles can arise. Finally, two simulation examples are given to verify the effectiveness of the proposed approach.

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A simple noniterative method to accurately calculate the centroid of an interval type‐2 fuzzy set

Arman

2022

Int J of Intelligent Sys

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An interval type‐2 fuzzy set (IT2FS) contains the infinite number of embedded membership functions (MFs) defined as type‐1 fuzzy sets. The center of gravity (COG) of an IT2FS is obtained by integrating the centroids of all these MFs. However, obtaining the COG of an IT2FS in a continuous domain is impossible because the number of embedded MFs is infinite and, in a discrete domain, comes with exponential time complexity. Therefore, different algorithms were proposed to find the center of centroids (COCs) instead of the COG. These algorithms do not necessarily obtain the exact value of COC; they compete to find a more accurate result in less time. In this study, we propose a simple noniterative method to obtain the COG of IT2FSs. This method only considers the MFs which form the boundary values, that is, the lower MF (LMF) and upper MF (UMF), and obtains their centroids separately. We show that the COG of an IT2FS is equal to the weighted sum of the centroids of its LMF and UMF if the relative areas of LMF and UMF are considered their corresponding weights. We call this method the Indirect COG (ICOG) method because it indirectly obtains the COG of an IT2FS. This method finds the accurate COG of an IT2FS by considering only two MFs instead of infinite MFs. It can also obtain the accurate COG of an uncommon polygonal IT2FS schematically. We use numerical examples to illustrate that the ICOG obtains the accurate COG of an IT2FS very fast in a nonexponential time. We also develop a new triangular interval type‐2 fuzzy analytical hierarchy process that uses the ICOG method to accurately defuzzify the IT2 fuzzy weights.

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On Nie-Tan Operator and Type-Reduction of Interval Type-2 Fuzzy Sets

Cited by 68 publications

References 23 publications

Interval type‐2 fuzzy Kalman filter aided individual channel estimation in MIMO relay systems

Interval type‐2 fuzzy Kalman filter aided individual channel estimation in MIMO relay systems

Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

A simple noniterative method to accurately calculate the centroid of an interval type‐2 fuzzy set

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