A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator...
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![Page 1: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/1.jpg)
A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator
Author: Shi-Jay ChenSpeaker: Shih-Hua Wei2006 IEEE International Conference on Fuzzy SystemsSheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006
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outline
1. Introduction
2. Preliminaries
3. Analysis of the existing similarity measure
4. A new method to calculate the degree of similarity between fuzzy numbers based on geometric-mean averaging operator
5. A comparison of the similarity measure
6. Conclusions
![Page 3: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/3.jpg)
1. Introduction
Degree of similarity of fuzzy numbers is very important Decision making Fuzzy risk analysis Information fusion
![Page 4: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/4.jpg)
2. Preliminaries
Geometric mean
![Page 5: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/5.jpg)
Preliminaries
Generalized fuzzy numbers
![Page 6: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/6.jpg)
Hsieh-and-Chen’s Similarity Measure Hsieh and Chen presented a similarity measure between
fuzzy numbers. This method is based on the “graded mean integration representation distance”.
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![Page 7: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/7.jpg)
Lee’s Similarity Measure
Lee presented a similarity measure between trapezoidal normal fuzzy numbers for aggregating individual fuzzy opinions.
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![Page 8: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/8.jpg)
Chen-and-Chen’s Similarity Measure Chen and Chen presented a similarity measure between
generalized trapezoidal fuzzy numbers. It combined the concepts of the geometric distance and the center of gravity (COG) distance.
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![Page 9: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/9.jpg)
Yong et al. Similarity Measure
Yong et al. presented a method to measure the degree of similarity based on the radius of gyration points.
![Page 10: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/10.jpg)
3. Analysis of the existing similarity measure
Chen and Chen described the three properties, denoted as follows:
Chen and Chen cannot correctly handle two different generalized fuzzy numbers having the same COG points.
![Page 11: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/11.jpg)
Yong et al. method has revealed that the ROG-based similarity measure still has the following drawbacks.
![Page 12: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/12.jpg)
![Page 13: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/13.jpg)
4. A new method to calculate the degree of similarity between fuzzy numbers based on geometric-mean averaging operator
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![Page 14: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/14.jpg)
5. A comparison of the similarity measure
![Page 15: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/15.jpg)
![Page 16: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/16.jpg)
![Page 17: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/17.jpg)
![Page 18: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/18.jpg)
![Page 19: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/19.jpg)
![Page 20: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/20.jpg)
![Page 21: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/21.jpg)
![Page 22: A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator Author: Shi-Jay Chen Speaker: Shih-Hua Wei 2006 IEEE International.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f155503460f94c2b0f5/html5/thumbnails/22.jpg)
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5. Conclusions
This study presented a new method for calculating the similarity measure of generalized fuzzy numbers. Some properties of the proposed similarity measure were demonstrated, and 26 sets of generalized fuzzy numbers were adopted to compare the proposed similarity measure with five existing similarity measures. Figure 7 and Table I indicate that the proposed similarity measure can overcome the drawbacks of the existing similarity measures.