Although numerous research studies in recent years have been proposed for comparing and ranking fuzzy numbers, most of the existing approaches suffer from plenty of shortcomings. In particular, they have produced counter-intuitive ranking orders under certain cases, inconsistent ranking orders of the fuzzy numbers' images, and lack of discrimination power to rank similar and symmetric fuzzy numbers. This study's goal is to propose a new epsilon-deviation degree approach based on the left and right areas of a fuzzy number and the concept of a centroid point to overcome previous drawbacks. The proposed approach defines an epsilon-transfer coefficient to avoid illogicality when ranking fuzzy numbers with identical centroid points and develops two innovative ranking indices to consistently distinguish similar or symmetric fuzzy numbers by considering the decision maker's attitude. The advantages of the proposed method are illustrated through several numerical examples and comparisons with the existing approaches. The results demonstrate that this approach is effective for ranking generalized fuzzy numbers and overcomes the shortcomings in recent studies.