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 Conference on Fuzzy Systems Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006

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

1. Introduction Degree of similarity of fuzzy numbers is very important Decision making Fuzzy risk analysis Information fusion

2. Preliminaries Geometric mean

Preliminaries Generalized fuzzy numbers

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”. Triangular form: Trapezoidal form:

Lee’s Similarity Measure Lee presented a similarity measure between trapezoidal normal fuzzy numbers for aggregating individual fuzzy opinions. where l p and U of discourse are defined as follows:

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.

Yong et al. Similarity Measure Yong et al. presented a method to measure the degree of similarity based on the radius of gyration points.

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.

Yong et al. method has revealed that the ROG-based similarity measure still has the following drawbacks.

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

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.