Quasi-homogeneous associative functions

Abstract

A triangular norm is a special kind of associative function on the closed unit interval [0,1]. Triangular norms (or t-norms) were introduced in the context of probabilistic metric space theory, and they have found applications also in other areas, such as fuzzy set theory. We determine the explicit forms of all t-norms which satisfy a generalized homogeneity property called quasi-homogeneity.

Keywords

• Triangular norm (t-norm)
• homogeneous function
• probabilistic metric space.