Ranking of fuzzy numbers by a new metric

In this paper, a new approach for comparison among fuzzy numbers based on new metric distance (D _TM) is proposed. All reasonable properties of ranking function are proved. At first, the distance on the interval numbers based on convex hall of endpoints is proposed. The existing distance measures for interval numbers, (Bardossy and Duckstein in Fuzzy rule-based modeling with applications to geophysical, biological and engineering systems. CRC press, Boca Raton, 1995; Diamond in Info Sci 46:141–157, 1988; Diamond and Korner in Comput Math Appl 33:15–32, 1997; Tran and Duckstein in Fuzzy Set Syst 130:331–341, 2002; Diamond and Tanaka Fuzzy regression analysis. In: Slowinski R (ed) Fuzzy sets in decision analysis, operations research and statistics. Kluwer, Boston, pp 349–387, 1998) do not satisfy the properties of a metric distance, while the proposed distance does. It is extended to fuzzy numbers and its properties are proved in detail. Finally, we compare the proposed definition with some of the known ones.