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A duality between fuzzy domains and strongly completely distributive $L$-ordered sets | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 11، شماره 4، آبان 2014، صفحه 23-43 اصل مقاله (461.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1622 | ||
| نویسندگان | ||
| W. Yao1؛ B. Zhao* 2 | ||
| 1Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China | ||
| 2Department of Mathematics, Shaanxi Normal University, Xi'an 710062, P.R. China | ||
| چکیده | ||
| The aim of this paper is to establish a fuzzy version of the duality between domains and completely distributive lattices. All values are taken in a fixed frame $L$. A definition of (strongly) completely distributive $L$-ordered sets is introduced. The main result in this paper is that the category of fuzzy domains is dually equivalent to the category of strongly completely distributive $L$-ordered sets. The results in this paper establish close connections among fuzzy-set approach of quantitative domains and fuzzy topology with modified $L$-sober spaces and spatial $L$-frames as links. In addition, some mistakes in [K.R. Wagner, Liminf convergence in $\Omega$-categories, Theoretical Computer Science 184 (1997) 61--104] are pointed out. | ||
| کلیدواژهها | ||
| Fuzzy DCPO؛ Fuzzy domain؛ Fuzzy Scott topology؛ (Spatial) $L$-frame؛ $L$-frame homomorphism؛ (Strongly) Completely distributive $L$-ordered set؛ Modified $L$-sober | ||
| مراجع | ||
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