A New Similarity Measure Between Interval-Valued Trapezoidal Fuzzy Numbers Based on Geometric Distance and the Center-of-Gravity-Points

2007 ◽  
Author(s):  
Shih-Hua Wei ◽  
Shyi-Ming Chen
Keyword(s):  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Center Of Gravity ◽  
Geometric Distance ◽  
Trapezoidal Fuzzy Numbers ◽  
Interval Valued

scholarly journals Ranking and Similarity Measures of Interval-Valued Pentagonal Fuzzy Numbers

2019 ◽  
Vol 8 (4) ◽  
pp. 9314-9320
Keyword(s):  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Flow Chart ◽  
Geometric Distance ◽  
Signed Distance ◽  
Mathematical Formulas ◽  
Interval Valued

We define generalized interval-valued pentagonal fuzzy numbers. Based on the height of the lower and upper pentagonal fuzzy numbers we propose to categorize interval-valued pentagonal fuzzy numbers into three different categories. Using signed distance concept de-fuzzification of interval-valued pentagonal fuzzy numbers is proposed and mathematical formulas are derived using   cut representations. We also introduce two similarity measures for interval-valued pentagonal fuzzy numbers based on geometric distance, area and height of pentagonal fuzzy numbers and geometric distance, perimeter and height of pentagonal fuzzy numbers respectively. Algorithms for finding de-fuzzification value and similarity measures are proposed with flow-chart illustration.

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