Additive and multiplicative generators in interval-valued fuzzy set theory

In this paper, we introduce the notion of additive and multiplicative generator on L^I, which is the underlying lattice of interval-valued fuzzy set theory. A special class of generators on L^I is the class of representable generators which can be represented using generators on the unit interval. A representation of involutive negators on L^I by means of continuous additive generators which is similar to the representation of involutive negators on the unit interval is given. We also investigate additive and multiplicative generators of t-norms on L^I