Document Type : Research Paper

**Authors**

Institute of Math., school of Math. and Computer Sciences, Nanjing Normal University, Nanjing Jiangsu 210046, People0 s Republic of China

**Abstract**

In this paper, a new definition of fuzzy bounded sets and totally

fuzzy bounded sets is introduced and properties of such sets are studied. Then

a relation between totally fuzzy bounded sets and N-compactness is discussed.

Finally, a geometric characterization for fuzzy totally bounded sets in I- topological

vector spaces is derived.

fuzzy bounded sets is introduced and properties of such sets are studied. Then

a relation between totally fuzzy bounded sets and N-compactness is discussed.

Finally, a geometric characterization for fuzzy totally bounded sets in I- topological

vector spaces is derived.

**Keywords**

[1] S. Z. Bai, Some properties of near SR -compactness, Iranian Journal of Fuzzy Systems, 4(2)

(2007), 83-87.

[2] J. X. Fang, On local bases of fuzzy topological vector space, Fuzzy Sets and Systems, 87

(1997), 341-347.

[3] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157(20)

(2006), 2739-2750.

[4] J. X. Fang and C. H. Yan, L-fuzzy topological vector spaces, J. Fuzzy Math., 5(1) (1997),

133-144.

[5] U. H¨ohle and S. E. Rodabaugh(Eds.), Mathematics of fuzzy set: logic, topology and measure

theory, the handbook of fuzzy sets series, Kluwer Academic Publisher, Dordrecht, 3 (1999).

[6] A. K. Katsaras, Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 6 (1981), 85-95.

[7] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984),

143-154.

[8] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J.

Math. Anal. Appl., 58 (1997) 135-146.

[9] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1997.

(2007), 83-87.

[2] J. X. Fang, On local bases of fuzzy topological vector space, Fuzzy Sets and Systems, 87

(1997), 341-347.

[3] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157(20)

(2006), 2739-2750.

[4] J. X. Fang and C. H. Yan, L-fuzzy topological vector spaces, J. Fuzzy Math., 5(1) (1997),

133-144.

[5] U. H¨ohle and S. E. Rodabaugh(Eds.), Mathematics of fuzzy set: logic, topology and measure

theory, the handbook of fuzzy sets series, Kluwer Academic Publisher, Dordrecht, 3 (1999).

[6] A. K. Katsaras, Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 6 (1981), 85-95.

[7] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984),

143-154.

[8] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J.

Math. Anal. Appl., 58 (1997) 135-146.

[9] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1997.

[10] A. Narayanan and S. Vijayabalaji, Intuitionistic fuzzy bounded linear operators, Iranian

Journal of Fuzzy Systems, 4(1) (2007), 89-101.

[11] P. M. Pu and Y. M. Liu, Fuzzy topology I, neighborhood structure of a fuzzy point and

Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.

[12] D. W. Qiu, Fuzzifying topological linear spaces, Fuzzy Sets and Systems, 147 (2004), 249-272.

[13] G. J. Wang, A new compactness defined by fuzzy sets, J. Math. Anal. Appl., 94 (1983), 1-23.

[14] R. H. Warren, Neighborhoods bases and continuity in fuzzy topological spaces, Rocky Mountain

J. Math., 8 (1978), 459-470.

[15] C. X. Wu and J. X. Fang, A new definition of Fuzzy topological vector space, Science

Exploration (China), 4 (1982), 113-116.

[16] J. R. Wu, Fuzzy totally bounded sets, J. Suzhou Institute of Urban Construction and Environment

Protection (China), 11 (1998), 8-12.

[17] C. H. Yan, Two generating mappings !L and L in complete lattices TVS and LFTVS., J.

Fuzzy Math., 6(3) (1998) 745-750.

[18] C. H. Yan and J. X. Fang, Generalization of Kolmogoroff’s theorem to L-topological vector

spaces, Fuzzy Sets and Systems, 125(2) (2002), 177-183.

[19] C. H. Yan and J. X. Fang, Generalization of inductive topologies to L-topological vector

spaces, Fuzzy Sets and Systems, 131(3) (2002), 347-352.

[20] C. H. Yan and J. X. Fang, L-fuzzy bilinear operator and its continuity, Iranian Journal of

Fuzzy Systems, 4(1) (2007), 65-73.

[21] H. Zhang and J. X. Fang, On locally convex I-topological vector spaces, Fuzzy Sets and

Systems, 157(14) (2006), 1995-2002.

[22] H. P. Zhang and J. X. Fang, Local convexity and local boundedness of induced I(L)- topological

vector spaces, Fuzzy Sets and Systems, 158(13) (2007), 1496-1503.

Journal of Fuzzy Systems, 4(1) (2007), 89-101.

[11] P. M. Pu and Y. M. Liu, Fuzzy topology I, neighborhood structure of a fuzzy point and

Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.

[12] D. W. Qiu, Fuzzifying topological linear spaces, Fuzzy Sets and Systems, 147 (2004), 249-272.

[13] G. J. Wang, A new compactness defined by fuzzy sets, J. Math. Anal. Appl., 94 (1983), 1-23.

[14] R. H. Warren, Neighborhoods bases and continuity in fuzzy topological spaces, Rocky Mountain

J. Math., 8 (1978), 459-470.

[15] C. X. Wu and J. X. Fang, A new definition of Fuzzy topological vector space, Science

Exploration (China), 4 (1982), 113-116.

[16] J. R. Wu, Fuzzy totally bounded sets, J. Suzhou Institute of Urban Construction and Environment

Protection (China), 11 (1998), 8-12.

[17] C. H. Yan, Two generating mappings !L and L in complete lattices TVS and LFTVS., J.

Fuzzy Math., 6(3) (1998) 745-750.

[18] C. H. Yan and J. X. Fang, Generalization of Kolmogoroff’s theorem to L-topological vector

spaces, Fuzzy Sets and Systems, 125(2) (2002), 177-183.

[19] C. H. Yan and J. X. Fang, Generalization of inductive topologies to L-topological vector

spaces, Fuzzy Sets and Systems, 131(3) (2002), 347-352.

[20] C. H. Yan and J. X. Fang, L-fuzzy bilinear operator and its continuity, Iranian Journal of

Fuzzy Systems, 4(1) (2007), 65-73.

[21] H. Zhang and J. X. Fang, On locally convex I-topological vector spaces, Fuzzy Sets and

Systems, 157(14) (2006), 1995-2002.

[22] H. P. Zhang and J. X. Fang, Local convexity and local boundedness of induced I(L)- topological

vector spaces, Fuzzy Sets and Systems, 158(13) (2007), 1496-1503.

September and October 2009

Pages 73-90