Preference relation on fuzzy utilities based on fuzzy leftness relation on intervals

We define a new preference relation /spl mu/p(x, y) between two fuzzy numbers or utilities x and y, based on the fuzzy leftness-relationship between intervals. A key property of /spl mu/p(x, y) is that it satisfies the well-known min-transitivity property: /spl mu/p(x, z) > mini/spl mu/p(x, y), /spl mu/p(y, z)); the previous definitions of preference relation for fuzzy utilities satisfy only certain weaker forms of transitivity.