有界格上一致模的构造

发布时间：2018-03-21 13:50

  本文选题：有界格　切入点：一致模　出处：《山东大学》2017年硕士论文　论文类型：学位论文

【摘要】：由Yager与Rybolov提出的一致模算子是一类重要的聚合算子,是三角模与三角余模的推广和一致化.由于一致模具有很多良好的性质,故其被广泛地应用于信息聚合、模糊系统模型、神经网络等领域,具有十分重要的理论和应用价值.一致模的构造是研究一致模需要解决的首要问题.关于一致模的构造已经有很多的结果,但这些研究多是限制在单位闭区间或者是有限链上.最近,定义在有界格上一致模算子的构造越来越受到人们的关注.一方面,有界格打破了单位闭区间或是有限链上全序关系的限制,拓宽了一致模的应用领域;另一方面,有界格又是单位闭区间或有限链的概括.本文主要讨论了有界格上一致模的构造,主要的研究工作与结果如下:1.给出了一般有界全序集上的一致模的构造.2.引入了一维单位区间映射的概念,证明了一维单位区间映射是一个序同构映射,由此将满足一维单位区间映射的有界全序集与([0,1],≤ 建立格同构,从而将单位区间[0,1]上定义的一致模的性质几乎完全转移到满足条件的有界全序集上.3.探讨了一般有界格上一致模的构造情况,试图说明,一般有界格上的一致模的构造的形式有限,想要进一步研究有界格上一致模的情况,需要对有界格加以其他的条件.4.构造了满足条件Ie=(?)的有界格上的一致模,并给出了一般有界格转化为Ie=(?)的有界格的方法.5.在有界格上引入二维单位区间映射的概念,将满足条件的有界格与二维闭区间格建立格同构.
[Abstract]:The uniform module operator proposed by Yager and Rybolov is a kind of important aggregation operator, which is the generalization and uniformity of triangular module and triangle comodule. Because of its many good properties, uniform mold is widely used in information aggregation and fuzzy system model. The construction of uniform modules is the most important problem to be solved in the study of uniform modules. There have been many results on the construction of uniform modules. Recently, the construction of uniformly modular operators defined on bounded lattices has attracted more and more attention. Bounded lattices break the restriction of the totally ordered relations on unit closed intervals or finite chains, and widen the application fields of uniform modules; on the other hand, Bounded lattices are generalizations of unit closed intervals or finite chains. In this paper, we mainly discuss the construction of uniform modules on bounded lattices. The main research work and results are as follows: 1. The construction of uniform modules on a general bounded totally ordered set is given. The concept of one-dimensional unit interval mapping is introduced, and it is proved that one-dimensional unit interval mapping is an ordered isomorphic map. Therefore, the bounded totally ordered set satisfying one-dimensional unit interval mapping is isomorphic to ([0 ~ 1], 鈮，

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