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INTUITIONISTIC FUZZY QUASI-METRIC AND PSEUDO-METRIC SPACES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 5، شماره 3، دی 2008، صفحه 81-88 اصل مقاله (214.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2008.349 | ||
| نویسندگان | ||
| Yongfa Hong* 1؛ Xianwen Fang2؛ Binguo Wang1 | ||
| 1College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong, 266510, P. R. China | ||
| 2Department of Mathematics and Physics, Anhui University of Science and Technology, Huainan,Anhui, 232001, P. R. China | ||
| چکیده | ||
| In this paper, we propose a new definition of intuitionistic fuzzy quasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. We prove some properties of intuitionistic fuzzy quasi- metric and pseudo-metric spaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionistic fuzzy regular and intuitionistic fuzzy completely normal and hence intuitionistic fuzzy normal. These are the intuitionistic fuzzy generalization of the corresponding properties of fuzzy quasi-metric and pseudo- metric spaces. | ||
| کلیدواژهها | ||
| Intuitionistic fuzzy quasi-metric spaces؛ Intuitionistic fuzzy pseudometric spaces | ||
| مراجع | ||
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[1] K. T. Atanassov, Intuitionistic fuzzy sets, Central Tech. Library, Bulgarian Academy Science, Sofia, Bulgaria, Rep. No. 1697/84, 1983. [2] K. T. Atanassov, Intuitionistic fuzzy sets, Heidelberg, Germany: Physica-Verlag, 1999. [3] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88(1) (1997), 81 -89. [4] J. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145-74. [5] V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 28(4) (2006), 902-905. [6] F. G. Lupia˜nez, Nets and filters in intuitionistic fuzzy topological spaces, Information Sciences 176(16) (2006), 2396-2404. [7] N. Palaniappan, Fuzzy topology, CRC Press, 2002. [8] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5) (2004), 1039-46. [9] R. Saadati, A. Razani and H. Adibi, A common fixed point theorem in L-fuzzy metric spaces, Chaos, Solitons & Fractals, 33(2) (2007), 358-363. [10] R. Saadati, Notes to the paper ”Fixed points in intuitionistic fuzzy metric spaces” and its generalization to L- fuzzy metric spaces, Chaos, Solitons & Fractals, 35(1) (2008), 176-180. [11] R. Saadati, On the L-fuzzy topological spaces, Chaos, Solitons & Fractals, In Press, 37(5) (2008), 1419-1426. [12] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353. | ||
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