Affiliations: Fuzziness and Uncertainty Modelling Research Unit,
Department of Mathematics and Computer Science, Ghent University, Belgium
Note: [] Corresponding author: Department of Applied Mathematics and
Computer Science, Ghent University, Krijgslaan 281 (S9), B – 9000 Gent,
Belgium. E-mail: glad.deschrijver@ugent.be
Abstract: 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], ⩽).
Keywords: t-norm on L[TeX:] ^I, arithmetic operations on L[TeX:] ^I, addition, subtraction, multiplication, division
