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This paper deals with the problem of the ranking of generalized fuzzy numbers. Our aim is to give a possibility to rank any non-identical generalized fuzzy numbers. The majority of existing approaches fail to rank fuzzy numbers in certain cases and give equality when in fact fuzzy numbers are different. We explore and extend Chen and Lu's approach that is good enough in terms of computational effort and efficiency in case of large quantity of fuzzy numbers. Chen and Lu's algorithm ranks fuzzy numbers based on the left and right dominance established by Â¿-cuts. The only drawback of this algorithm is that it does not differentiate fuzzy numbers in some situations. We suggest an extension of the algorithm to solve this problem. We apply our algorithm to fuzzy risk analysis problems, particularly those concerning risks to choose among several alternatives.