Generalized arithmetic operations in interval-valued fuzzy set theory

We generalize the addition, subtraction, multiplication and division on L $^{I}$ defined in [4], where L $^I$ is the underlying lattice of both interval-valued fuzzy set theory [14] and intuitionistic fuzzy set theory [1]. We investigate some algebraic properties of these operations. We show that using these operations some important t-norms on L $^I$ and some related operations can be written in a similar way as their counterparts on ([0,1], ⩽).