本文選題：有界格　切入點：一致模　出處：《山東大學》2017年碩士論文　論文類型：學位論文

【摘要】：由Yager與Rybolov提出的一致模算子是一類重要的聚合算子,是三角模與三角余模的推廣和一致化.由于一致模具有很多良好的性質(zhì),故其被廣泛地應用于信息聚合、模糊系統(tǒng)模型、神經(jīng)網(wǎng)絡等領域,具有十分重要的理論和應用價值.一致模的構(gòu)造是研究一致模需要解決的首要問題.關于一致模的構(gòu)造已經(jīng)有很多的結(jié)果,但這些研究多是限制在單位閉區(qū)間或者是有限鏈上.最近,定義在有界格上一致模算子的構(gòu)造越來越受到人們的關注.一方面,有界格打破了單位閉區(qū)間或是有限鏈上全序關系的限制,拓寬了一致模的應用領域;另一方面,有界格又是單位閉區(qū)間或有限鏈的概括.本文主要討論了有界格上一致模的構(gòu)造,主要的研究工作與結(jié)果如下:1.給出了一般有界全序集上的一致模的構(gòu)造.2.引入了一維單位區(qū)間映射的概念,證明了一維單位區(qū)間映射是一個序同構(gòu)映射,由此將滿足一維單位區(qū)間映射的有界全序集與([0,1],≤ 建立格同構(gòu),從而將單位區(qū)間[0,1]上定義的一致模的性質(zhì)幾乎完全轉(zhuǎn)移到滿足條件的有界全序集上.3.探討了一般有界格上一致模的構(gòu)造情況,試圖說明,一般有界格上的一致模的構(gòu)造的形式有限,想要進一步研究有界格上一致模的情況,需要對有界格加以其他的條件.4.構(gòu)造了滿足條件Ie=(?)的有界格上的一致模,并給出了一般有界格轉(zhuǎn)化為Ie=(?)的有界格的方法.5.在有界格上引入二維單位區(qū)間映射的概念,將滿足條件的有界格與二維閉區(qū)間格建立格同構(gòu).
[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，

本文編號：1644130