关于带有连续基础算子的一致模的若干问题研究

发布时间：2018-01-11 15:11

本文关键词：关于带有连续基础算子的一致模的若干问题研究　出处：《山东大学》2016年博士论文　论文类型：学位论文

【摘要】：聚合算子是关于信息融合的数学模型,其作用是将多个输入信息融合后得到单个输出。在实际应用中,聚合算子的构造与选择是一项繁杂且重要的工作。选取合理的聚合算子对于信息融合至关重要,它决定了融合效果的优劣。一致模作为聚合算子家族中的一个重要成员,具有优良的代数性质,在各领域有着广泛的应用。已有的文献研究大多局限于讨论常见的一致模的结构、特征刻画和相关函数方程等。本文专注于带有连续基础算子的一致模的研究,主要研究带有连续基础算子的一致模的特征刻画及其关于连续三角余模的分配性问题。本文工作分为三部分：第一部分研究其特征刻画及相关一致模的构造方法；第二部分研究带有连续基础算子的一致模关于连续三角余模的分配性和条件分配性问题；第三部分研究带有光滑基础算子的离散一致模的特征刻画问题。主要内容如下：绪论部分介绍本文的研究背景及创新之处。预备知识部分介绍本文涉及到的概念、专业术语及相关主要结论。第二章研究带有连续基础算子的一致模的特征刻画问题。本章给出带有严格基础算子一致模的完全特征刻画,从而完善Fodor和De Baets的研究结论,进一步刻画带有连续、阿基米德基础算子的一致模；给出带有幂等基础三角模或基础三角余模的一致模的完全特征刻画。另一方面,基于以上的特征刻画结论,本章提出两种构造一致模的方法,并给出相应的充要条件。这些特征刻画和方法均有助于聚合算子的构造及选取问题的解决。第三章研究一致模关于连续三角余模的分配性问题。一致模关于连续三角余模的分配性和条件分配性方程的求解,是Klement在Linz2000会议上重申的公开问题之一。这一问题与伪分析、积分聚合算子的构造有着紧密的联系。基于常见一致模,Ruiz和Torrens给出了分配性及条件分配性方程的解,并证明了一致模关于连续三角余模的分配性方程和条件分配性方程是等价的。本章突破已有研究成果的限制,研究带有连续基础算子的一致模关于连续三角余模的分配性和条件分配性方程,得到相应的部分解：若带有连续基础算子的一致模关于连续三角余模是条件分配的,则连续三角余模为取大算子或其序和结构中至多有一个加数；若连续三角余模为严格的,则满足条件分配性方程的一致模必定为可表示一致模；若连续三角余模为幂零的,则不存在满足条件分配性方程的一致模；若连续三角余模具有序和结构时,给出满足条件分配性方程的一致模所应满足的部分性质。本章进一步证明带有连续基础算子的一致模关于连续三角余模的分配性方程和条件分配性方程是等价的。本文的研究成果进一步完善了Ruiz和Torrens的结论,为Klement公开问题的完整解决又迈近了的一步。第四章研究定义在有限链上的离散一致模。在模糊控制等实际问题中,往往需要限制在有限链上进行一致模的研究。相关文献已经详细讨论了常见一致模在有限链上的对应形式。本章研究带有连续基础算子的一致模在有限链上的对应形式：带有光滑基础算子的离散一致模,分析其代数性质：在A(e)内离散一致模取小或取大,并进一步给出其基于三个一元函数的完全特征刻画,为一致模的实际应用提供了坚实的理论基础。
[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.

【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP202

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