L-FUZZY BILINEAR OPERATOR AND ITS CONTINUITY

Document Type: Research Paper

Authors

Department of Mathematics, Nanjing Normal University, Nanjing Jiangsu, 210097, P.R.China

Abstract

The purpose of this paper is to introduce the concept of L-fuzzy
bilinear operators. We obtain a decomposition theorem for L-fuzzy bilinear
operators and then prove that a L-fuzzy bilinear operator is the same as a
powerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).
Finally we discuss the continuity of L-fuzzy bilinear operators.

Keywords


[1] Jin-xuan Fang, Fuzzy linear order-homomorphism and its structures, The Journal of Fuzzy
Mathematics, 4(1)(1996), 93–102.
[2] Jin-xuan Fang, The continuity of fuzzy linear order-homomorphisms, The Journal of Fuzzy
Mathematics, 5(4)(1997), 829–838.
[3] Jin-xuan Fang and Cong-hua Yan, L-fuzzy topological vector spaces, The Journal of Fuzzy
Mathematics, 5(1)(1997), 133–144.
[4] He Ming, Bi-induced mapping on L-fuzzy sets, KeXue TongBao 31(1986) 475(in Chinese).
[5] U. H¨ohle and S. E. Rodabaugh, eds., Mathematics of fuzzy sets: logic, topology and measure
theory, The handbooks of Fuzzy Sets Series, Vol. 3(1999), Kluwer Academic Publishers
(Dordrecht).
[6] Ying-ming Liu and Mao-kang Luo, Fuzzy topology, World Scientific Publishing, Singapore,
1997.

[7] S. E. Rodabaugh, Point-set lattice-theoretic topology, Fuzzy Sets and Systems, 40(1991),
297–347.
[8] S.E.Rodabaugh, Powerset operator foundations for point-set lattice-theoretic(Poslat) fuzzy
set theories and topologies, Questions Mathematicae, 20(1997), 463–530.
[9] Guo-jun Wang, Order-homomorphism of fuzzes, Fuzzy Sets and Systems, 12(1984), 281–288.
[10] Guo-jun Wang, Theory of L-fuzzy topological spaces, Shanxi Normal University Publishing
House, 1988 (in Chineses).
[11] Cong-hua Yan, Initial L-fuzzy topologies determined by the family of L-fuzzy linear orderhomomorphims,
Fuzzy Sets and Systems, 116(2000), 409–413.
[12] Cong-hua Yan, Projective limit of L-fuzzy locally convex topological vector spaces, The Journal
of Fuzzy Mathematics, 9(2001), 89-96.
[13] Cong-hua Yan, Generalization of inductive topologies to L-topological vector spaces, Fuzzy
Sets and Systems, 131(3)(2002), 347–352.
[14] Cong-hua Yan and Jin-xuan Fang, L-fuzzy locally convex topological vector spaces, The Journal
of Fuzzy Mathematics, 7(1999), 765–772.
[15] Cong-hua Yan and Jin-xuan Fang, The uniform boundedness principle in L-topological vector
spaces, Fuzzy Sets and Systems, 136(2003), 121–126.
[16] Cong-hua Yan and Cong-xin Wu, Fuzzy L-bornological spaces, Information Sciences,
173(2005), 1–10.
[17] L.A. Zadeh, Fuzzy sets, Information and Control, 8(1965), 338–353.