Introduction
The problem of comparing imprecise or uncertain quantities has been attempted by many researchers. In literature, as much as 40 schemes for ranking fuzzy quantities have been presented during last three decades with a lot of debates and contradictory claims. Inconsistency of the ranking orders among different approaches and the debates thereon were due to the different criteria of selections. Given two imprecise quantities, it is assumed that a set of precisely defined decision objectives are needed in order to decide, which of the two precedes or ranks above the other, or, which of the notions – the notion of preference or the notion of greater than (or less than) – is to be given the priority, or, whether an optimally selected (greatest/lowest) set satisfies an intuitive notion of being the most preferred (Wang & Kerre (1996, 2001a, 2001b)). In fuzzy literatures, we find some remarkable research papers that categorize and compare ranking strategies implicitly or explicitly on the basis of some criteria, such as the distinguishability (Bortolan & Degani (1985)), the rationality (Nakamura (1986)), and the fuzzy or linguistic presentation (Tong & Bonissone (1980) and Delgado et al. (1988)).
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Sengupta, A., Pal, T.K. (2009). On Comparing Interval Numbers: A Study on Existing Ideas. In: Fuzzy Preference Ordering of Interval Numbers in Decision Problems. Studies in Fuzziness and Soft Computing, vol 238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89915-0_2
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