Min-transitivity of fuzzy leftness relationship and its application to decision making

We show that the fuzzy leftness relationship Left(A, B) between two intervals A and B on a line, which we had recently defined for modeling spatial relationships, satisfies the min-transitivity property. The previous definitions of leftness given by Krishnapuram et al. and Miyajima et al. do not have this property. The min-transitivity property plays an important role in fuzzy decision making based on Orlovsky's result. We give several general schemes for constructing concrete min-transitive relations based on our Left(A, B) for use in fuzzy decision making. (C) 1997 Elsevier Science B.V.