On fuzzy number lattice (R̃, ≤)

We give a systematic development of fuzzy number lattice theory. Many of our results generalize to number lattice over the lattice algebra. Our first main result is that the real number chain (R, ≤) is a homomorphic image of the fuzzy number lattice (R̃, ≤) (that is, R̃/Θ ≅ R), and the congruence class [á]Θ(∀ãεR̃) is a component of (R̃, ≤). Thus, we can be specialized to describe the structure of the fuzzy number lattice (R̃, ≤). Next we study the structure and representation of the congruence class [ã].