“…the following conditions are satised, 2 A sample of the literature on fuzzy preferences is Orlovsky (1978), Ovchinnikov (1981), Basu (1984), Billot (1995), Dutta, Panda, Pattanaik (1986), Dutta (1987), Jain (1990), Ponsard (1990), Dasgupta and Deb (1991, 1996), Roubens (1991, 1992) and Banerjee (1993Banerjee ( , 1994. The philosophical underpinnings of these ideas are discussed in Piggins and Salles (2007).…”