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CHARACTERIZATIONS OF (L;M)-FUZZY TOPOLOGY DEGREES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 15، شماره 4، مهر و آبان 2018، صفحه 129-149 اصل مقاله (474.75 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.4121 | ||
| نویسندگان | ||
Yu Zhong1؛ Fu-Gui Shi  2
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| 1College of Science, North China University of Technology, Beijing, P. R. China | ||
| 2School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China. | ||
| چکیده | ||
| In this paper, characterizations of the degree to which a mapping $\mathcal{T} : L^{X}\longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail. What is more, the degree to which an $L$-subset is an $L$-open set with respect to $\mathcal{T}$ is introduced. Based on that, the degrees to which a mapping $f: X\longrightarrow Y$ is continuous, open, closed or a quotient mapping with respect to $\mathcal{T}_{X}$ and $\mathcal{T}_{Y}$ are defined, and their characterizations are given, respectively. Besides, the relationships among the continuity degrees, the openness degrees, the closedness degrees and the quotient degrees of mappings are discussed. | ||
| کلیدواژه‌ها | ||
| $(L؛ M)$-fuzzy topology degree؛ $L$-open set degree؛ Continuity degree؛ Openness degree؛ Closedness degree؛ Quotient degree | ||
| مراجع | ||
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