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

Abstract

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