Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\\ Vector Spaces
نویسندگان
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
doi
10.22111/ijfs.2014.1400چکیده
In this paper, a new definition of bounded fuzzy linear orderhomomorphism on $I$-topological vector spaces is introduced. Thisdefinition differs from the definition of Fang [The continuity offuzzy linear order-homomorphism. J. Fuzzy Math. {\bf5}\textbf{(4)}(1997), 829--838]. We show that the ``boundedness"and `` boundedness on each layer" of fuzzy linear orderhomomorphisms do not imply each other. On the basis,characterizations of continuity of fuzzy linearorder-homomorphisms, and the relation between continuity andboundedness are studied.
