A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers

A New Similarity Function for Generalized Trapezoidal Fuzzy Numbers

“…The fifth property holds only partially, since there are other pairs of fuzzy numbers whose similarity is zero in addition to the numbers A = (0,0, 0,0; 0) and B = (1,1,1,1;1) 4. T he proposal has the following property: ba,a,a,a; 0) (a,a,a,a;e)) = e -^ 0 (( ' li'm ",, 1and b\\a,a,a,a;0) (a,a,a,a;e)) = 0, which overcomes that drawe -^ 1 back of the measures proposed by Chen and Chen [2] and Wei and Chen [12], outlined in Section 2.…”

“…For example, the similarity between A = (a, a, a, a; 0) and B = (a, a, a, a; 10-^° ) is S(A, B) « 1, which appears to be more reasonable than the null value assigned by the measures proposed by Chen and Chen [2] and Wei and Chen [12]. As the spheres in the Euclidean distance in R^ are circles, if we represent the circle centered at the centroid of (0,0,0,0), i.e.…”

“…This action effectively mitigates the drawback of the measures by Chen and Chen [2] and Wei and Chen [12], since it assigns a high degree of similarity to fuzzy numbers of the form (a, a, a, a, 0) and (a, a, a, a, e) with e near zero, and also provides a new property: , then the degree of similarity of C and A with respect to B, with w = 0.5, is 0.7156 in both cases. Therefore, the numbers C and A are just similar to the central number B.…”

“…Wei and Chen [12] proposed a new measure using the perimeter concept of generalized trapezoidal fuzzy numbers:…”

“…For instance, a nine-member linguistic terms set is introduced in [12]. These linguistic terms are usually associated with a triangular or trapezoidal fuzzy number [15].…”