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L-FUZZY BILINEAR OPERATOR AND ITS CONTINUITY | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 4، شماره 1، تیر 2007، صفحه 65-73 اصل مقاله (205.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2007.358 | ||
| نویسندگان | ||
Cong-hua Yan  ؛ Jin-xuan Fang
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| Department of Mathematics, Nanjing Normal University, Nanjing Jiangsu, 210097, P.R.China | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Order-homomorphism؛ Powerset operator؛ L-bilinear operator؛ Molecule net | ||
| مراجع | ||
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[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. | ||
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