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

Document Type: Research Paper


1 School of Mathematical Science, Nanjing Normal University, Nan- jing, Jiangsu 210023, P. R. China

2 Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000, P. R. China


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.


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