Additive generators in interval-valued fuzzy set theory

Glad Deschrijver.

In this paper we study generators of t-norms on the lattice LI of closed subintervals of the unit interval. Starting from a minimal set of axioms that any addition and multiplication operator on LI must fulfill, we investigate the properties of the additive and multiplicative generators on LI obtained using these arithmetic operators. We also investigate under which conditions the generators on LII generate a t-norm.

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