粗糙S-系和模糊S-系

【作者】 孙玉峰；

【导师】 谢祥云；

【作者基本信息】 五邑大学 ， 应用数学， 2008， 硕士

【摘要】 我们首先引入了粗糙S-系和模糊S-系的概念,然后讨论了粗糙S-系的性质,比较详细地介绍了在S-子系诱导的同余下的粗糙S-系的性质,以及两个粗糙S-子系得直积的上、下近似集的性质;我们重点讨论了模糊S-系的交和并的上、下近似集的性质。在第二章中我们介绍了S-系上模糊同余的概念,讨论了S-系上模糊同余和模糊等价关系间的联系;重点讨论了由S-系上的任意模糊二元关系生成的模糊同余的结构和性质;在介绍了模糊同余类后,我们证明了S-系上的模糊同态定理以及模糊Rees同余的性质。在第三章中,我们给出了模糊素S-系和模糊半素S-系的定义,并研究了它们的上、下近似集的性质,然后讨论了模糊素S-系和模糊半素S-系的扩张性质。最后,我们证明了:如果模糊S-系f是模糊不可约的,那么对于f模糊素性和模糊半素性是等价的;另外,利用模糊素S-系给出半群中的素理想的一个等价刻画。更多还原

【Abstract】 In this paper,we introduce the notions of approximate S-acts and fuzzy S-acts,and discuss some of their properties.Specially,we investigate the characters of approximate S-act under a congruence induced by a S-subact.The properties which are of the upper and lower approximation sets of the products of S-acts,the union and meet of two fuzzy S-subacts,are also discussed.In chapter two,we give the definitions of fuzzy congruences on a S-act,and we discuss the relations between fuzzy congruences and fuzzy equivalences;we obtain the properties of fuzzy Rees congruences;and fuzzy morphisms theorem of S-acts.In chapter three,we introduce the concepts of fuzzy prime(semiprime)S-acts,and investigate the properties of their upper and lower approximate sets.Then we discuss the extension properties of fuzzy prime(semiprime)S-acts.Finally,we prove that a fuzzy irreducible semiprime S-act must be a fuzzy prime S-act;and give an equivalent description of prime ideals of semigroups by using fuzzy prime S-acts.更多还原