Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets
نویسندگان
1 Department of Mathematics and Physics, Wuyi University , Jiangmen, Guangdong, 529020, P.R.China
2 Jian Tang\\ School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, 236041, P.R.China
doi
10.22111/ijfs.2010.180چکیده
Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper, the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two main theorems which characterize regular orderedsemigroups and intra-regular ordered semigroups in terms of fuzzyleft ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzyquasi-ideals are given. The paper shows that one can pass fromresults in terms of fuzzy subsets in semigroups to orderedsemigroups. The corresponding results of unordered semigroups arealso obtained.
