Fuzzy理想和Fuzzy幂零根

本文给出了Ｆ—准素（ＦＷ—准素）理想的有限交是Ｆ－准素理想（ＦＷ－准素理想）的几个充分条件。此外，证明了［５］中定义的一个交换环Ｒ的Ｆｕｚｚｙ幂零根是Ｒ的幂零根Ｋ的特征函数Ｘ＿Ｋ。

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.

半群中一些特殊Fuzzy双理想之间的关系

讨论了半群S中,P为S的Fuzzy弱素双理想与其t截集Pt(t>0)为素双理想之间的关系,以及Fuzzy完全素双理想与Fuzzy素双理想的关系,并证明了在正则交换半群中,P为S的Fuzzy完全素双理想当且仅当P为半群S的Fuzzy素双理想;P为S的Fuzzy弱完全素双理想当且仅当P为半群S的Fuzzy弱素双理想.

Characterisations of semigroups by the properties of their picture fuzzy bi-ideals

In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.

弱MTL代数的演绎系统与同余关系的对应定理

通过在剩余格L中引入条件:a,b∈L,(a→(a→b))∨(b→(b→a))=1,建立弱MTL代数结构,讨论弱MTL代数中极大(素)演绎系统和极大(素)同余关系的基本性质以及两者之间的联系,证明了弱MTL代数中(极大,素)同余关系与(极大,素)演绎系统一一对应。