ON FUZZY NUMBER LATTICE ((R)OVER-TILDE, LESS-THAN-OR-EQUAL-TO)

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, less than or e qual to) is a homomorphic image of the fuzzy number lattice ((R) over tilde, less than or equal to) (that is, (R) over tilde/Theta congruent to R), and the congruence class [(a) over tilde]Theta(For All (a) ove r tilde is an element of (R) over tilde) is a component of ((R) over t ilde, less than or equal to). Thus, we can be specialized to describe the structure of the fuzzy number lattice ((R) over tilde, less than o r equal to). Next we study the structure and representation of the con gruence class [(a) over tilde]. (C) 1997 Elsevier Science B.V.