PROCEEDINGS IPMU '08

Additive generators in interval-valued fuzzy set theory

Glad Deschrijver.

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

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