Lattice-valued interval sets and t-representable interval set t-norms

Interval sets were proposed by Yiyu Yao in 1993. Interval set theory is related to interval analysis, rough set, fuzzy set and flou set, it can be regarded as a new tool for representing incomplete and uncertain information. In this paper, we introduce the notion of lattice-valued interval set, and investigate its basic algebra operations. We divide the operations into two kinds: inducible and non-inducible. Moreover, we propose the notion t-representable interval set t-norms, and prove a fundamental theorem related residuated implication of t-representable interval set t-norms.