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Rough approximation operators based on quantale-valued fuzzy generalized neighborhood systems | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 16، شماره 6، بهمن و اسفند 2019، صفحه 53-63 اصل مقاله (208.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2019.5019 | ||
| نویسندگان | ||
| F. F. Zhao* 1؛ L. Q. Li1؛ S. B. Sun2؛ Q. Jin1 | ||
| 1Department of Mathematics, Liaocheng University, Liaocheng, P.R.China | ||
| 2School of Computer Science and Technology, Liaocheng University, Liaocheng, P.R.China | ||
| چکیده | ||
| Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhood system is introduced and then a pair of lower and upper approximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system-based approximation operators, $L$-fuzzy relation-based approximation operators and $L$-fuzzy covering-based approximation operators as their special circumstances. Therefore, the research on $L$-fuzzy generalized neighborhood system-based approximation operators has more general significance. In addition, when the $L$-fuzzy generalized neighborhood system is serial, reflexive, unary and transitive, then the corresponding approximation operators are discussed and characterized, respectively. | ||
| کلیدواژهها | ||
| Fuzzy rough set؛ fuzzy topology؛ $L$-fuzzy generalized neighborhood system؛ quantale | ||
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