Implicative Ideals and Fuzzy Implicative Ideals of a Distributive Implication Groupoid

We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient conditions for an ideal (fuzzy ideal) to be an implicative ideal (fuzzy implicative ideal) is given. By using the concept of level sets, we will characterize the fuzzy implicative ideals of a distributive implication groupoid. Finally, an extension property for fuzzy implicative ideals is given.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

广义模糊子半环的广义模糊双(内)理想

给出了广义模糊子半环的广义模糊双(内)理想的概念.运用截集、模糊子集的和与积得到了广义模糊子半环的广义模糊双(内)理想的等价条件及性质,同时还得到了在半环的同态映射下同态像及同态原像的性质.当λ=0,μ=1时,得到一般意义下的模糊子半环的模糊双(内)理想的相应结果.     

Fuzzy半群中的Fuzzy理想

本文先引入Ｆｕｚｚｙ半群中Ｆｕｚｚｙ理想的概念，进而讨论它们的一些代数性质，推广了前人的一些结果。     

格的模糊软理想

将模糊软集与格的模糊理想概念相结合,引入了格的模糊软理想的概念,给出了它们的若干代数性质.定义了格的模糊软同态(同构)概念,证明了格的一个模糊软理想在模糊软同构(同态)下的像(原像)仍为模糊软理想的结论.     

半群的模糊理想和模糊同余

引入半群上模糊理想、模糊同余的概念。给出它们的一些等价刻划,证明了一个半群上所有模糊同余关系作成一个格。最后,给出模糊理想的积和模糊同余关系的积的概念,讨论了它们的一些性质。     

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。     

Fuzzy半群中的极小Fuzzy理想

本文先给出Ｆｕｚｙ半群中极小Ｆｕｚｙ理想的一些代数性质,进而利用极小Ｆｕｚｙ理想刻划Ｆｕｚｚｙ单半群的一些代数性质     

Fuzzy semirings

In this paper we initiate the study of fuzzy semirings and fuzzy A-semimodules where A is a semiring and A-semimodules are representations of A. In particular, semirings all of whose ideals are idempotent, called fully idempotent semirings, are investigated in a fuzzy context. It is proved, among other results, that a semiring A is fully idempotent if and only if the lattice of fuzzy ideals of A is distributive under the sum and product of fuzzy ideals. It is also shown that the set of proper fuzzy prime ideals of a fully idempotent semiring A admits the structure of a topological space, called the fuzzy prime spectrum of A.     

格蕴涵代数的关联理想与模糊关联理想(英文)

本文提出了格蕴涵代数的关联理想和模糊关联理想的概念 ,讨论了它们的性质 ,指出了关联理想与理想、关联理想与关联滤子、关联理想与模糊关联理想、模糊关联理想与模糊关联滤子、模糊关联理想与模糊理想之间的关系     

非对合剩余格的正规双极值模糊理想

本文对非对合剩余格的双极值模糊理想问题作进一步深入研究.引入了非对合剩余格的正规双极值模糊理想概念, 考察了其性质并获得了其若干等价刻画.同时, 给出了两类特殊的双极值模糊理想的定义, 分别称为极大双极值模糊理想和完全正规双极值模糊理想并讨论了它们的性质和相互关系.这些工作为进一步揭示非对合剩余格的结构特征拓展了研究思路.     

The Rough Intuitionistic Fuzzy Ideals of Intuitionistic Fuzzy Subrings in a Commutative Ring

The aim of this paper is to give some definitions of rough intuitionistic fuzzy ideal, rough intuitionistic fuzzy radical, rough prime (primary) intuitionistic fuzzy ideal and rough semiprime intuitionistic fuzzy ideal of an intuitionistic fuzzy subring, and also to give some properties of such ideals. Moreover, we give their nature under homomorphism.     

布尔代数的直觉T-S模糊子代数及理想

在布尔代数中引入了的直觉T-S模糊子代数和直觉T-S模糊理想的概念,给出了布尔代数的直觉T-S模糊子代数的两个等价定义,进一步讨论了它们的性质.证明了布尔代数的两个直觉T-S模糊子代数(理想)的模交与直积也是直觉T-S模糊子代数(理想).     

New Kinds of Fuzzy Ideals in BCI-algebras*

Following the seminal work of Xi on the definition of fuzzy ideal in BCI-algebras, three new kinds of definitions of fuzzy ideal of BCI-algebras are proposed. First, by the use of the relations between fuzzy points and fuzzy sets, the definition of a (s,t]-fuzzy ideals of BCI-algebras is introduced. The acceptable nontrivial concepts obtained in this manner are the - fuzzy ideals and -fuzzy ideals. Second, based on the concept of falling shadow, a theoretical approach of fuzzy ideal is established and the fuzzy ideal based on t-norm is proposed. Finally, by the use of the implication operators of fuzzy logic, an R-fuzzy ideals is proposed and relations between the (s,t]-fuzzy ideals and R-fuzzy ideals are discussed. *Foundation Item:Supported by NNSF of China(60274016). Biography:Zhang Guang-ji(1947-),male,Professor     

环R的质Fuzzy理想

本文分析了文［３］中Ｆｕｚｚｙ质理想定义之不足，给出了质Ｆｕｚｚｙ理想的概念，讨论了它的等价刻划及性质。     

半群中的粗糙模糊理想及粗糙模糊素理想

将粗糙集的理论方法用于模糊半群的研究。给出上(下)粗模糊子半群及上(下)粗模糊左(右)理想、粗糙模糊素理想等概念,研究它们的有关性质。证明上粗模糊子半群与上粗模糊理想是通常的模糊子半群与模糊理想概念的扩张。     

Fuzzy Ideals and Fuzzy Interior Ideals in Ordered Semirings

The notions of fuzzy ideals and fuzzy interior ideals in ordered semirings are introduced and some of their characterizations are obtained through regularity criterion and with some operations on them.     

亚BCI-代数的模糊理想

引入了亚BCI-代数的模糊子代数、模糊理想、闭模糊理想和模糊P-理想的概念,研究了它们的性质。证明了模糊子代数(模糊理想、闭模糊理想、模糊P-理想)的同态像与同态原像仍能成为模糊子代数(模糊理想、闭模糊理想、模糊P-理想)。     

Fuzzy Ideals and Fuzzy Distributive Lattices

Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved.     

Fuzzy半群中的Fuzzy素理想

探讨Fuzzy半群中Fuzzy素理想,Fuzzy 完全理想与Fuzzy理想的根的一些代数性质,证明Fuzzy半群中每一个Fuzzy理想是Fuzzy完全半素理想当且仅当它可表为一族Fuzzy完全素理想之交。