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 ([0,1],les). A representation of involutive negators on L I by means of continuous additive generators which is similar to the representation of involutive negators on ([0,1], les) is given. We also investigate additive and multiplicative generators of t-norms on L I