A new approach to similarity measure for generalized trapezoidal fuzzy numbers and its application to fuzzy risk analysis

A new similarity measure has been proposed in this paper for generalized trapezoidal fuzzy numbers (GTrFNs). Here, the proposed similarity measure has been devised based on exponent distance, area, perimeter and height of a GTrFN. Most of the researchers described the similarity measure between two GTrFNs whose components belong to [0, 1] only. But the components of GTrFNs should be any real numbers belonged to R. For this reason, in this paper a similarity measure technique has been framed newly on GTrFN whose components are any real number which is the most important consideration here. Depending on the proposed method of similarity measure, some essential properties have been illustrated in this paper. Also, this method has been compared with some existing techniques of similarity measure taking twenty five different sets of GTrFNs. Henceforth, it is obtained that our proposed technique is better than other existing techniques. Finally, the proposed similarity measure has been applied in fuzzy risk analysis in a production system which has been described with numerical illustration.