This contribution is concerned with a detailed investigation of linearity axioms for fuzzy orderings. Different existing concepts are evaluated with respect to three fundamental correspondences from the classical case—linearizability of partial orderings, intersection representation, and one-to-one correspondence between linearity and maximality. As a main result, we obtain that it is virtually impossible to simultaneously preserve all these three properties in the fuzzy case. If we do not require a one-to-one correspondence between linearity and maximality, however, we obtain that an implication-based definition appears to constitute a sound compromise, in particular, if Łukasiewicz-type logics are considered. Key words: completeness, fuzzy ordering, fuzzy preference modeling, fuzzy relation,

Lipschitzian and kernel aggregation operators with respect to the natural T-indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator with respect to T.

Abstract — This paper presents an approach to a system based on fuzzy logic for the design of interpolative curves and surfaces in the context of Computer Aided Geometric Design (CAGD). Some problems arising from a previous model are studied by using a similarity approach.