本文關(guān)鍵詞：關(guān)于帶有連續(xù)基礎(chǔ)算子的一致模的若干問(wèn)題研究　出處：《山東大學(xué)》2016年博士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 一致模 分配性方程 三角余模 有限鏈 連續(xù)

【摘要】：聚合算子是關(guān)于信息融合的數(shù)學(xué)模型,其作用是將多個(gè)輸入信息融合后得到單個(gè)輸出。在實(shí)際應(yīng)用中,聚合算子的構(gòu)造與選擇是一項(xiàng)繁雜且重要的工作。選取合理的聚合算子對(duì)于信息融合至關(guān)重要,它決定了融合效果的優(yōu)劣。一致模作為聚合算子家族中的一個(gè)重要成員,具有優(yōu)良的代數(shù)性質(zhì),在各領(lǐng)域有著廣泛的應(yīng)用。已有的文獻(xiàn)研究大多局限于討論常見(jiàn)的一致模的結(jié)構(gòu)、特征刻畫(huà)和相關(guān)函數(shù)方程等。本文專(zhuān)注于帶有連續(xù)基礎(chǔ)算子的一致模的研究,主要研究帶有連續(xù)基礎(chǔ)算子的一致模的特征刻畫(huà)及其關(guān)于連續(xù)三角余模的分配性問(wèn)題。本文工作分為三部分：第一部分研究其特征刻畫(huà)及相關(guān)一致模的構(gòu)造方法；第二部分研究帶有連續(xù)基礎(chǔ)算子的一致模關(guān)于連續(xù)三角余模的分配性和條件分配性問(wèn)題；第三部分研究帶有光滑基礎(chǔ)算子的離散一致模的特征刻畫(huà)問(wèn)題。主要內(nèi)容如下：緒論部分介紹本文的研究背景及創(chuàng)新之處。預(yù)備知識(shí)部分介紹本文涉及到的概念、專(zhuān)業(yè)術(shù)語(yǔ)及相關(guān)主要結(jié)論。第二章研究帶有連續(xù)基礎(chǔ)算子的一致模的特征刻畫(huà)問(wèn)題。本章給出帶有嚴(yán)格基礎(chǔ)算子一致模的完全特征刻畫(huà),從而完善Fodor和De Baets的研究結(jié)論,進(jìn)一步刻畫(huà)帶有連續(xù)、阿基米德基礎(chǔ)算子的一致模；給出帶有冪等基礎(chǔ)三角�；蚧A(chǔ)三角余模的一致模的完全特征刻畫(huà)。另一方面,基于以上的特征刻畫(huà)結(jié)論,本章提出兩種構(gòu)造一致模的方法,并給出相應(yīng)的充要條件。這些特征刻畫(huà)和方法均有助于聚合算子的構(gòu)造及選取問(wèn)題的解決。第三章研究一致模關(guān)于連續(xù)三角余模的分配性問(wèn)題。一致模關(guān)于連續(xù)三角余模的分配性和條件分配性方程的求解,是Klement在Linz2000會(huì)議上重申的公開(kāi)問(wèn)題之一。這一問(wèn)題與偽分析、積分聚合算子的構(gòu)造有著緊密的聯(lián)系�；诔Ｒ�(jiàn)一致模,Ruiz和Torrens給出了分配性及條件分配性方程的解,并證明了一致模關(guān)于連續(xù)三角余模的分配性方程和條件分配性方程是等價(jià)的。本章突破已有研究成果的限制,研究帶有連續(xù)基礎(chǔ)算子的一致模關(guān)于連續(xù)三角余模的分配性和條件分配性方程,得到相應(yīng)的部分解：若帶有連續(xù)基礎(chǔ)算子的一致模關(guān)于連續(xù)三角余模是條件分配的,則連續(xù)三角余模為取大算子或其序和結(jié)構(gòu)中至多有一個(gè)加數(shù)；若連續(xù)三角余模為嚴(yán)格的,則滿足條件分配性方程的一致模必定為可表示一致模；若連續(xù)三角余模為冪零的,則不存在滿足條件分配性方程的一致模；若連續(xù)三角余模具有序和結(jié)構(gòu)時(shí),給出滿足條件分配性方程的一致模所應(yīng)滿足的部分性質(zhì)。本章進(jìn)一步證明帶有連續(xù)基礎(chǔ)算子的一致模關(guān)于連續(xù)三角余模的分配性方程和條件分配性方程是等價(jià)的。本文的研究成果進(jìn)一步完善了Ruiz和Torrens的結(jié)論,為Klement公開(kāi)問(wèn)題的完整解決又邁近了的一步。第四章研究定義在有限鏈上的離散一致模。在模糊控制等實(shí)際問(wèn)題中,往往需要限制在有限鏈上進(jìn)行一致模的研究。相關(guān)文獻(xiàn)已經(jīng)詳細(xì)討論了常見(jiàn)一致模在有限鏈上的對(duì)應(yīng)形式。本章研究帶有連續(xù)基礎(chǔ)算子的一致模在有限鏈上的對(duì)應(yīng)形式：帶有光滑基礎(chǔ)算子的離散一致模,分析其代數(shù)性質(zhì)：在A(e)內(nèi)離散一致模取小或取大,并進(jìn)一步給出其基于三個(gè)一元函數(shù)的完全特征刻畫(huà),為一致模的實(shí)際應(yīng)用提供了堅(jiān)實(shí)的理論基礎(chǔ)。
[Abstract]:Aggregation operator is on the mathematical model of information fusion, its role is to a plurality of input information fusion obtained after a single output. In practical application, polymerization structure and selection operator is a complicated and important work. Choosing reasonable aggregation operator for information fusion is very important, it determines the effect of fusion uninorm. As an important member of the family aggregation operator the algebraic properties has excellent, is widely used in various fields. The structure of the existing research is mostly limited to discuss common uninorm, characterization and correlation function equation. This study focused on uninorm operator with continuous basis, consistent characteristics the main research model with continuous operator based characterization and distribution of issues on continuous t-conorms. This paper is divided into three parts: the first part of its characterization The construction method and correlation consistent mode; the second part of the study with continuous uninorm operator based on the continuous t-conorms distribution and conditional distribution problems; the third part studies the characteristics of the discrete model is consistent with the basic characterization of the smooth operator. The main contents are as follows: the introduction part introduces the research background and prepare the innovation of this paper. This paper introduces the concept of knowledge related to the professional terms and related main conclusions. The second chapter studies the characteristics of uninorm operator with continuous based characterization of the problem. This chapter gives a complete characterization of feature based operator to strict mode, so as to improve the results of Fodor and De Baets, to further characterize with continuous uninorm, Archimedes basic operator; complete characterization of uninorm features give a basic triangular norm or idempotent based S-norm. On the other hand, radical From the above characterization results, this chapter puts forward two methods to construct uniform modules, and gives the necessary and sufficient conditions. These features and methods are helpful to resolve the problem of selection of structure and aggregation operators. The distribution of the third chapter research mode on continuous t-conorms. Solving the uniform norm on continuous triangle conorm distributive and conditional distribution equation, is one of the open problems in Klement Linz2000. The meeting reiterated this issue with the pseudo analysis, integral aggregation operators are closely linked. The common consensus model based on Ruiz and Torrens, given the distribution and conditional distribution of equation, and prove the same model on continuous t-conorms distribution equation and conditional distribution equation is equivalent to the existing research results. This chapter breaks through the limitation of uninorm with continuous operator on continuous basis T-conorms distribution and conditional distribution equation, get the corresponding solution: if the uninorm operator with continuous based on continuous t-conorms is the conditional distribution, then continuous t-conorms for maximum operator or its sequence and structure in at least one addend; if three consecutive corner die strictly, satisfy uninorm conditions distributive equations must be consistent if the continuous mode can be expressed; t-conorms is nilpotent, there is no consistent mode distributive equations; if continuous t-conorms with sequence and structure, some properties are uniformly distributive equations of the die should be satisfied. This chapter further proves the uniform norm with continuous operator based on continuous t-conorms distribution equation and conditional distribution equation are equivalent. The results of this study to further improve the Ruiz and Torrens, For the complete Klement open problem solved the last step step. The fourth chapter studies the definition in the discrete finite chain uninorm. In practical problems such as fuzzy control, often need to limit the study of consistent mode in finite chain. The related literature is discussed in detail in the corresponding form on a finite chain common agreement the corresponding form in the model. On the finite chain uninorm this chapter studies with continuous basis operators: discrete uninorm operator with smooth basis, analyze its algebraic properties in A (E) in discrete uninorm small or large, and further gives the characteristics based on three element function description that provides a solid theoretical foundation for the practical application of uninorm.

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：TP202

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本文編號(hào)：1410045