A Novel Similarity Measure for Generalized Trapezoidal Fuzzy Numbers and its Application to Decision-Making

2016 ◽  
Vol 9 (3) ◽  
pp. 131-148 ◽  
Author(s):  
Yixiang Zhou
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Numbers ◽  
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.

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