Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\\ Vector Spaces

In this paper, a new definition of bounded fuzzy linear order homomorphism on $I$-topological vector spaces is introduced. This definition differs from the definition of Fang [The continuity of fuzzy linear order-homomorphism. J. Fuzzy Math. {\bf 5}\textbf{(4)}(1997), 829--838]. We show that the ``boundedness" and `` boundedness on each layer" of fuzzy linear order homomorphisms do not imply each other. On the basis, characterizations of continuity of fuzzy linear order-homomorphisms, and the relation between continuity and boundedness are studied.