A new method for trapezoidal fuzzy numbers ranking based on the Shadow length and its application to manager's risk taking

Ranking of fuzzy numbers is one of the practicable operators, which plays an important role in fuzzy mathematical, decisions and engineering procedures. There is considerable work in ranking of fuzzy numbers that have been improved over time. However, some strong ranking methods need to calculate complex and lengthy mathematical calculations in their ordering processes. In this paper, we represent a novel ranking method of trapezoidal/triangular fuzzy numbers TFNs based on the Shadow length, which is simply coded in any programming language. On the other hand, many fuzzy numbers ranking methods give the same order for fuzzy numbers in any level of manager's risk taking. So we insert the risk taking factor RF to order fuzzy numbers and provide a reasonable range of fuzzy numbers comparison through wide levels of this factor. Furthermore, we apply and compare several useful examples and ranking methods to depict the reasonable performance of our proposed method.

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