Ranking fuzzy numbers using reference sets and degree of dominance

Ranking fuzzy numbers plays a critical role in decision analysis under a fuzzy environment. Existing fuzzy ranking methods may not always be suitable for practical decision problems of large size, due to counter-intuitive ranking outcomes produced or considerable computational effort required. This paper presents an effective approach to address the fuzzy ranking problem of practical size. The proposed approach combines the merits of two prominent concepts individually used in the literature: the fuzzy reference set and the degree of dominance. As such, the decisive information embedded in the set of fuzzy numbers to be ranked is sensibly used, and satisfactory ranking outcomes are always achieved. The approach is computationally simple and its underlying concepts are logically sound and comprehensible. A comparative study is conducted on all benchmark cases used in the literature to examine its performance on rationality and discriminatory ability. The comparison result shows that the approach compares favorably with comparable methods examined