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Generalization of rough fuzzy sets based on a fuzzy ideal | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 20، شماره 1، فروردین و اردیبهشت 2023، صفحه 27-38 اصل مقاله (185.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7344 | ||
| نویسندگان | ||
| I. Ibedou* 1؛ S. E. Abbas2 | ||
| 1Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt | ||
| 2Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt | ||
| چکیده | ||
| Since Pawlak defined the notion of rough sets in 1982, many authors made wide research studying rough sets in the ordinary case and the fuzzy case. This paper introduced a new style of rough fuzzy sets based on %arbitrary fuzzy relation $R$ and a fuzzy ideal $\ell$ on a universal finite set $X$. New lower and new upper fuzzy sets are introduced, and consequently, fuzzy interior and fuzzy closure operators of a rough fuzzy set are discussed. These definitions, if $\ell$ is restricted to $\ell^{\circ} = \{\overline{0}\}$, imply the fuzzification of previous definitions given in the ordinary case, and moreover in the crisp case, we get exactly these previous definitions. The new style gives us a better accuracy value of roughness than the previous styles. Rough fuzzy connectedness is introduced as a sample of applications on the recent style of roughness. | ||
| کلیدواژه‌ها | ||
| Fuzzy approximation space؛ rough set؛ rough fuzzy set؛ rough fuzzy connectedness | ||
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آمار تعداد مشاهده مقاله: 136 تعداد دریافت فایل اصل مقاله: 290 |
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