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Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 7، شماره 2، شهریور 2010، صفحه 121-140 اصل مقاله (248.49 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2010.180 | ||
| نویسندگان | ||
| Xiang-Yun Xie* 1؛ Jian Tang2 | ||
| 1Department of Mathematics and Physics, Wuyi University , Jiangmen, Guangdong, 529020, P.R.China | ||
| 2Jian Tang\\ School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, 236041, P.R.China | ||
| چکیده | ||
| Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is an arbitrary mapping from $S$ into $[0,1]$, where $[0,1]$ is the usual interval of real numbers. In this paper, the concept of fuzzy generalized bi-ideals of an ordered semigroup $S$ is introduced. Regular ordered semigroups are characterized by means of fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. Finally, two main theorems which characterize regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy quasi-ideals are given. The paper shows that one can pass from results in terms of fuzzy subsets in semigroups to ordered semigroups. The corresponding results of unordered semigroups are also obtained. | ||
| کلیدواژهها | ||
| Ordered semigroup؛ Regular ordered semigroup؛ Intra-regular ordered semigroup؛ Fuzzy left (right) ideal؛ Fuzzy (generalized) bi-ideal؛ Fuzzy quasi-ideal | ||
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