本文選題：邏輯等價算子 + 模糊推理��； 參考：《陜西師范大學(xué)》2015年博士論文

【摘要】：模糊推理是模糊控制的理論基礎(chǔ),魯棒性是評判模糊推理的重要標準.在討論魯棒性時,擾動參數(shù)的選取極為關(guān)鍵.我們常用的擾動參數(shù)大多是建立在[0,1]單位區(qū)間上通常度量的基礎(chǔ)之上.然而模糊推理的結(jié)果很大程度上取決于它的內(nèi)蘊結(jié)構(gòu),蘊涵算子和模糊連接詞.邏輯等價算子由蘊涵算子生成,因此用邏輯等價算子構(gòu)造的擾動參數(shù)討論魯棒性,與邏輯推理會更為和諧.本文的第一個研究目的在于借助邏輯等價算子構(gòu)造一系列的擾動參數(shù),進而討論三I推理方法的魯棒性.另一個研究目的在于借助拓撲學(xué)工具,對這些擾動參數(shù)作以比較,并對一些邏輯等價算子導(dǎo)出的相關(guān)拓撲性質(zhì)作以探討.全文共分四章：第一章首先介紹模糊推理的基本概念和若干重要的模糊推理方法,其次介紹剩余格和拓撲學(xué)的相關(guān)知識,為后面章節(jié)的研究作必要的準備.第二章首先借助邏輯等價算子定義了模糊集之間的平均邏輯相似度,并以這種平均邏輯相似度作為擾動參數(shù)討論了邏輯連接詞的魯棒性和三I推理方法的魯棒性.其次,將極小邏輯相似度和平均邏輯相似度從拓撲的角度做了比較,得出這兩種相似度導(dǎo)出的度量空間是等價的.最后,分析了不同的蘊涵算子導(dǎo)出的度量空間中孤立點的分布情況及連通性、稠密子集等性質(zhì).在此基礎(chǔ)上,對不同的相似度從擾動參數(shù)的角度作了比較.第三章首先將模糊集之間的極小邏輯相似度推廣到格值模糊集上,在此基礎(chǔ)上構(gòu)造了FL(X)上的拓撲空間,其中FL(X)代表論域X上取值于格L的格值模糊集的全體.指出了由R0蘊涵算子和Godel蘊涵算子所確定的拓撲空間中凝聚點是正規(guī)模糊集或其補集,但反之不真且構(gòu)造了反例.其次,當(dāng)L是剩余格時,借助邏輯等價算子和三角模,構(gòu)造出兩個格值相似度E1,E2,證明了這兩者均是L-等式,并指出Ei-Cauchy列是Ei-收斂列,i=1,2.再次,為了更直觀地表現(xiàn)兩個格值模糊集的相似程度,借助邏輯等價算子m和[0,1]MV上的態(tài)算子定義了取值于[0,1]的Ⅰ-Ⅳ型相似度：Sm,Sm,Sm*,和Sm,證明了它們滿足格值相似度的三條公理,并將Sm作為擾動參數(shù),討論了RL-型三I算法的魯棒性.在以上各種相似度的構(gòu)造中,剩余格上的兩種邏輯等價算子起著關(guān)鍵作用,我們從這兩個邏輯等價算子出發(fā)建立了剩余格上的-致拓撲和商剩余格.特別地,對[0,1]剩余格中不同的邏輯等價算子導(dǎo)出的度量空間的緊性和序列的收斂性做了詳細討論.第四章首先在完備格上分析了兩對剩余算子復(fù)合后的性質(zhì),給出了反例說明這種復(fù)合不具有還原性.討論了聚合雙極信息的雙極t-模和雙極蘊涵可以分解為兩個單級算子的條件,并給出了雙極信息在決策方面的一個應(yīng)用實例.表示雙極信息的工具之一就是雙極模糊集,雙極模糊集又稱為直覺模糊集.直覺模糊集作為特殊的格值模糊集有著特殊的應(yīng)用背景和性質(zhì).其次,借助邏輯等價算子,建立了直覺模糊集上的四類相似度并且詳細討論了其性質(zhì),繼而以這些相似度作為擾動參數(shù),從魯棒性分析的角度,對它們作了比較.最后,給出了一個模式識別問題的應(yīng)用實例.
[Abstract]:Fuzzy reasoning is the theoretical basis of fuzzy control. Robustness is an important criterion for evaluating fuzzy reasoning. When the robustness is discussed, the selection of disturbance parameters is very important. Most of the disturbance parameters we commonly use are based on the usual measurement in the [0,1] unit interval. However, the results of fuzzy reasoning largely depend on its internal parameters. Implication structure, implication operator and fuzzy connectives. Logic equivalent operators are generated by implication operators. Therefore, the disturbance parameters constructed by logical equivalence operators are more robust and more harmonious with logical reasoning. The first study of this paper is to construct a series of perturbation parameters with the aid of logical equivalence operator, and then discuss the three I reasoning method. Another research aim is to compare these disturbance parameters with the tools of topology and discuss the related topological properties derived from some logical equivalent operators. The full text is divided into four chapters. The first chapter first introduces the basic concepts of fuzzy reasoning and some important fuzzy reasoning methods. Secondly, the residual lattice and topology are introduced. In the second chapter, the average logical similarity between fuzzy sets is defined by the use of logical equivalence operators. The robustness of logical connectives and the robustness of the three I reasoning method are discussed with this average logical similarity as a disturbance parameter. Secondly, the minimal logic similarity is similar. The degree and the average logical similarity are compared from the topological point of view, and the measurement space derived from the two similarities is equivalent. Finally, the distribution of the isolated points in the metric spaces derived from the different implication operators and the properties of the dense subsets are analyzed. On this basis, the different similarity degrees are from the angle of the disturbance parameters. In the third chapter, the third chapter generalize the minimal logical similarity between the fuzzy sets to the Lattice valued fuzzy set. On this basis, the topological space on FL (X) is constructed, in which the FL (X) represents the Lattice valued fuzzy set of lattice L on the domain X. The aggregation points in the topological space determined by the R0 implication operator and Godel implication operator are pointed out. A normal fuzzy set or its complement, but vice versa is not true. Secondly, when L is a residual lattice, two lattice values similarity E1, E2 are constructed with the aid of logical equivalence operator and trigonometric model. It is proved that both of these are L- equations, and that the Ei-Cauchy column is a Ei- convergence column and i=1,2. again, in order to more intuitively show the similarity of the two Lattice valued fuzzy sets. Degree, by means of the state operators on logical equivalent operators m and [0,1]MV, I define the type I IV similarity degrees of value in [0,1]: Sm, Sm, Sm*, and Sm, and prove that they satisfy three axioms of the lattice value similarity, and discuss the robustness of the RL- type three I algorithm by using Sm as a perturbation parameter. In the construction of the above similarity, two kinds of logic on the residual lattice are constructed. The key role plays a key role. We set up the topological and quotient residual lattices on the remaining lattices from the two logical equivalence operators. In particular, the tightness and the convergence of the metric spaces derived from the different logical equivalent operators in the [0,1] residual lattices are discussed in detail. The fourth chapter first analyzes two pairs in the complete lattice. A counterexample is given to show that the compound is not reductive. The conditions for the bipolar t- mode and the bipolar implication to be decomposed into two single level operators are discussed, and an application example of the bipolar information in decision making is given. One of the tools for the bipolar information is a bipolar fuzzy set, The bipolar fuzzy sets are also called intuitionistic fuzzy sets. The intuitionistic fuzzy sets have special application background and properties as special Lattice valued fuzzy sets. Secondly, four kinds of similarity degrees on intuitionistic fuzzy sets are established with the help of logical equivalent operators and their properties are discussed in detail. Then, the angle of similarity is used as a perturbation parameter, from the angle of robustness analysis. Finally, a practical example of pattern recognition is given.
【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：O159;O231

【相似文獻】

相關(guān)期刊論文 前6條

1 吳望名;關(guān)于模糊邏輯的—場爭論[J];模糊系統(tǒng)與數(shù)學(xué);1995年02期

2 王永安;王國俊;楊合俊;;二值命題邏輯中命題真度相同與邏輯等價的關(guān)系[J];西安文理學(xué)院學(xué)報(自然科學(xué)版);2008年01期

3 孟令江;;一階邏輯推理系統(tǒng)F下量詞的性質(zhì)及運算規(guī)律[J];河北大學(xué)學(xué)報(自然科學(xué)版);2008年01期

4 劉劍凌;;否定效應(yīng)與邏輯等價——對沃森實驗的解釋[J];自然辯證法研究;2013年10期

5 何斌，王若恩;臨界概念和臨界命題[J];廣東工學(xué)院學(xué)報;1996年02期

6 ;[J];;年期

相關(guān)博士學(xué)位論文 前1條

1 段景瑤;邏輯等價算子在模糊推理中的應(yīng)用[D];陜西師范大學(xué);2015年

，

本文編號：1926487