An Improved Similarity Measure for Generalized Trapezoidal Fuzzy Numbers and Its Application in the Classification of EEG Signals

2021 ◽  
Author(s):  
Zhenya Qi
Keyword(s):  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Eeg Signals ◽  
Trapezoidal Fuzzy Numbers ◽  
Generalized Trapezoidal Fuzzy Numbers

New Similarity Measures Between Generalized Trapezoidal Fuzzy Numbers Using the Jaccard Index

2014 ◽  
Vol 22 (06) ◽  
pp. 831-844 ◽  
Author(s):  
Chao-Ming Hwang ◽  
Miin-Shen Yang
Keyword(s):  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Jaccard Index ◽  
Numerical Results ◽  
Trapezoidal Fuzzy Numbers ◽  
Generalized Trapezoidal Fuzzy Numbers

Similarity measures between generalized trapezoidal fuzzy numbers (GTFNs) are employed to indicate the degrees of similarity between GTFNs. Although several similarity measures of GTFNs have been proposed in the literature, none has considered using the Jaccard index. In general, the Jaccard index is a statistic used for comparing the similarity and diversity of sample sets. This paper presents a new similarity measure between GTFNs, which involves the Jaccard index. The proposed similarity measure is found to have better properties. Several examples are employed to compare the proposed measure with some existing methods. An experiment is performed using 15 sets of GTFNs to compare the proposed similarity measure with existing ones. Numerical results show that the proposed measure is more reasonable than those existing methods.

A distance and set theoretic-based similarity measure for generalized trapezoidal fuzzy numbers

2018 ◽  
Author(s):  
Sharifah Aniza Sayed Ahmad ◽  
Daud Mohamad ◽  
Nor Hashimah Sulaiman ◽  
Jamilah Mohd Shariff ◽  
Kamilah Abdullah
Keyword(s):  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers ◽  
Generalized Trapezoidal Fuzzy Numbers

scholarly journals A New Similarity Measure of Generalized Trapezoidal Fuzzy Numbers and Its Application on Rotor Fault Diagnosis

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xin Zuo ◽  
Lijun Wang ◽  
Yuanlong Yue
Keyword(s):  
Fault Diagnosis ◽  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Vital Role ◽  
Trapezoidal Fuzzy Numbers ◽  
Comparison Results ◽  
Rotor Experiment ◽  
Calculation Results ◽  
Generalized Trapezoidal Fuzzy Numbers

Fault diagnosis technology plays a vital role in the variety of critical engineering applications. Fuzzy approach is widely employed to cope with decision-making problems because it is in the simplest and most used form. This paper proposed a new similarity measure of generalized trapezoidal fuzzy numbers used for fault diagnosis. The presented similarity measure combines concepts of the geometric distance, the center of gravity point, the perimeter, and the area of the generalized trapezoidal fuzzy numbers for calculating the degree of similarity between generalized trapezoidal fuzzy numbers. This method is proposed to deal with both standardized and nonstandardized generalized trapezoidal fuzzy numbers. Some properties of the proposed similarity measure have been proved, and 12 sets of generalized fuzzy numbers have been used to compare the calculation results of the proposed similarity measures with the existing similarity measures. Comparison results indicate that the proposed similarity measure can overcome the drawbacks of existing similarity measures. Finally, a fault diagnosis experiment is carried out in laboratory based on multifunctional flexible rotor experiment bench. Experimental results demonstrate that the proposed similarity measure is more effective than other methods in terms of rotor fault diagnosis.

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