AHP多路径排序度量转换中的非线性问题

由于不同测量条件下的测量结果不是线性可加,AHP用矩阵乘法实现多路径序转换值得商榷.自隶属度从只取"1或0"两个值扩展到可取[0,1]区间上一切实数,可表征界于"是"与"不是"之间所有可能"部分是"模糊状态时起,对二值逻辑的研究已拓展到研究近似推理的模糊逻辑.这是逻辑的一个新的研究方向,目的是在隶属度转换过程中,通过对人类近似推理本领进行规范,使得到的目标值是"真值"在当前条件下的最优近似.模糊逻辑的量化方法是数值计算;推理依据是区分权滤波的冗余理论;实质性计算是由冗余理论导出的、实现隶属度转换的非线性去冗算法;所建的隶属度转换模型也是不同测量条件下高维状态空间上测量结果的非线性可加模型.将一维测量数据映射到高维状态空间上表为隶属度向量,可借助隶属度转换模型解决AHP多路径序转换的非线性计算.     

模糊综合评判加权平均模型的误导性阐释

模糊综合评判在不能界定隶属度转换是线性转换条件下,硬性用加权平均线性模型实现隶属度转换.通过揭示指标隶属度中通常包含确定目标隶属度不起作用的非线性冗余值,建立区分权滤波的冗余理论,用冗余理论界定隶属度转换不是线性转换,并构建近似推理逻辑支撑的隶属度转换模型.阐述所建模型为什么是当前条件下人们能构建的最优近似模型.当指标隶属度只取1或0两个值时模型将退化成模糊综合评判的"加权平均"模型.     

煤矿瓦斯风险评估中的多值逻辑

煤矿瓦斯风险评估中因风险状态渐变连续,所以单风险隶属度是可取[0,1]区间上一切实数,可表征"部分属于"模糊状态的模糊隶属度.因此由单风险隶属度确定多风险隶属度实现的是模糊状态转换,所以支撑隶属度转换的不是二值逻辑而是多值逻辑.在多值逻辑研究中,基于"取大取小"推理的模糊逻辑不是数学逻辑,"加权平均"的模糊综合评判是"假设"不是推理.所以处理模糊信息的多值逻辑尚需深入研究.指出隶属度转换不是线性转换的原因是,单风险模糊隶属度中可能包含对确定多风险隶属度不起作用的非线性冗余值.通过确定冗余值的数学表达式建立冗余理论,用冗余理论界定模糊隶属度转换不是线性转换,并推导去冗算法实现隶属度转换.由此建立处理模糊信息的多值逻辑.     

水质评价中的冗余理论与去余算法

水质评价在算法层面上解决的问题是,通过实现指标隶属度到目标隶属度转换确定目标水体的污染等级;存在的实质性问题是,如何界定隶属度转换不是简单的线性转换以及如何解决隶属度转换的非线性计算.为此,通过计算由隶属度向量表征的分类信息的信息熵、确定指标对水体分类所做贡献的大小;借助区分权概念揭示指标隶属度中包含对目标水体分类的冗余值.以"冗余"为切入点,建立以冗余定理、非线性转换等定理推论为基本内容的冗余理论.用冗余理论界定隶属度转换的非线性,建立基于区分权滤波的去余算法实现隶属度转换.所建模型在指标隶属度只取"0或1"两个数值时,将退化为通常的"加权平均"线性模型.     

支撑模糊集合转换的模糊逻辑是伪逻辑

模糊逻辑系统用模糊集合描述模糊信息、用模糊集合转换处理模糊信息.阐述支撑模糊集合转换的模糊逻辑为什么是伪逻辑的原因.指出定义在论域一个空间上的模糊集合,因为破坏了集合中元素的"不可分割性",所以模糊集合描述的模糊信息不能用数学计算通过模糊集合转换处理.实际应用中的模糊信息定义在论域与状态空间两个空间上,其正确表达方式是满足"归一化"条件的隶属度向量;处理的正确途径是,研究基于状态转移矩阵的隶属度转换;支撑隶属度转换的是近似推理逻辑,目的是使构建的隶属度转换模型是当前条件下人们可能构建的"最优"近似模型.     

基于非线性冗余算法的凝汽器状态评价

凝汽器状态评价指标是具有不同量纲的特征参数,为避免对具有不同量纲的特征空间实施无量纲化变换造成的信息失真,隶属度转换模式成为凝汽器状态评价的基本模式.由于特征参数状态渐变连续,所以表征参数状态的指标隶属度是模糊隶属度.模糊隶属度表征模糊状态,模糊隶属度转换实现模糊状态转换.用冗余理论界定模糊隶属度转换的非线性,用非线性去冗算法实现模糊隶属度转换并建立凝汽器状态评价的非线性评价模型.     

用模糊集合描述模糊信息的无效性

用模糊集合描述模糊信息无效的原因是,把原本是论域与状态空间上二元函数的模糊隶属函数看成是论域上的一元函数,用模糊集合描述的模糊信息,不能支持模糊集合转换;使得通过模糊集合转换处理模糊信息的模糊数学,不得不借用不是数学计算、无缘数学模型的"取大取小"实现模糊集合转换;结果是背离数学计算的模糊数学,不能为处理模糊信息提供算法支持,导致大量需要处理的模糊信息滞留至今.还原模糊信息是高维状态空间上分类数据的真实面目,把处理模糊信息明确为由指标隶属度确定目标隶属度的隶属度转换,是模糊数学回归数学的唯一正确途径.     

模糊CRI算法及模糊推理的有效性研究

通过揭示模糊推理的一种CRI算法的逻辑原理,提出了模糊推理的一种新算法.并对单规则的CRI算法(或三Ⅰ算法)的重心(或最大隶属度)去模糊法的有效性进行了研究.发现在单规则的CRI算法(或三Ⅰ算法)的模糊推理中,当大前提的后件取对称模糊集时,采用重心去模糊法使得推理结果无效,而采用最大隶属度去模糊法可使得推理结果有效.     

基于粗糙集知识约简的焊接动态过程建模

焊接过程的智能建模是焊接智能化技术的基础构成之一,将粗糙集理论应用在电弧焊接过程建模与成形质量预测方面.为提高计算效率,给出在不相容决策信息系统中基于最大近似质量和最大分类正确率的知识约简算法.在现有粗糙集建模方法的基础上,引入聚类分析、模糊逻辑及近似推理技术,提出一种改进的焊接动态过程建模方法,通过铝合金TIG焊接工艺实验验证模型的合理性及有效性.     

关于“模糊集的取大取小算法的不合理性”一文的商榷

周学松先生在《数学的实践与认识》期刊上发表了题为"模糊集的取大取小算法的不合理性"一文(2005,35(11):209-212),应用模糊命题逻辑讨论了取大取小算法不合理性的根本所在.从商榷周学松先生文中的某些论述和例证入手,对模糊集的取大取小算法进行辩证分析.     

一阶模糊谓词逻辑公式的解释模型真度理论及其应用

基于一阶模糊谓词逻辑公式的有限和可数解释真度的理论,引入了一阶模糊谓词逻辑公式的解释模型及解释模型真度的概念,并讨论了它们的一系列性质及其在近似推理中的应用.     

系统L_n中公式相对于有限理论的Г-绝对真度理论

将多值逻辑中的∑-α重言式理论与计量逻辑学中的真度理论相结合,在n值Lukasiewicz命题逻辑系统中引入了公式相对于有限理论Γ的Γ-绝对真度概念,讨论了它的若干性质.利用Γ-绝对真度定义了公式间的Γ-绝对相似度与伪距离,为进一步建立n值Lukasiewicz命题逻辑系统相对于有限理论Γ的近似推理奠定了基础.     

Theory of T-norms and fuzzy inference methods

In this paper, the theory of T-norm and T-conorm is reviewed and the T-norm, T-conorm and negation function are defined as a set of T-operators. Some typical T-operators and their mathematical properties are presented. Finally, the T-operators are extended to the conventional fuzzy reasoning methods which are based on the and operators. This extended fuzzy reasoning provides both a general and a flexible method for the design of fuzzy logic controllers and, more generally, for the modelling of any decision-making process.     

Well-Defined Fuzzy Sentential Logic

A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In the well-defined fuzzy sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning.     

Feasible algorithms for approximate reasoning using fuzzy logic

Deductive reasoning with classical logic is hampered when imprecision is present in the variables, although human reasoning can cope quite adequately with vague concepts. A new approach to reasoning which allows imprecise conclusions to be drawn consistently from imprecise premises was introduced by Baldwin [2]. This method is economical in calculation as it avoids the high dimensionality that fuzzy set representations often involve.This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method. A feasible algorithm for computing each process is then presented.It is assumed that the reader is familiar with the concept of, and operations on, fuzzy sets introduced by Zadeh [14].     

The case for an interval-based representation of linguistic truth

This paper develops an interval-based approach to the concept of linguistic truth. A special-purpose interval logic is defined, and it is argued that, for many applications, this logic provides a potentially useful alternative to the conventional fuzzy logic.The key idea is to interpret the numerical truth value v(p) of a proposition p as a degree of belief in the logical certainty of p, in which case p is regarded as true, for example, if v(p) falls within a certain range, say, the interval [0.7, 1]. This leads to a logic which, although being only a special case of fuzzy logic, appears to be no less linguistically correct and at the same time offers definite advantages in terms of mathematical simplicity and computational speed.It is also shown that this same interval logic can be generalized to a lattice-based logic having the capacity to accommodate propositions p which employ fuzzy predicates of type 2.     

数理逻辑中的数值化方法

数理逻辑的本质是形式推理而不是数值计算,非此即彼式的严谨性是其特征,因而在一定意义下它是"两极化"的.比如,(1)一个逻辑理论或者是相容的,或者是不相容的,不存在"半相容的"理论.(2)"逻辑公式A是假设集T的推论"或者成立,或者不成立,说它近似成立是无意义的.(3)逻辑公式中有重言式和矛盾式,但没有0.8重言式.本文的目的在于为上述基本概念提供程度化的版本,并从而建立一种近似推理理论.     

Fuzzy sets in approximate reasoning,Part 1: Inference with possibility distributions

A survey of about twenty years of approximate reasoning based on fuzzy logic and possibility theory is proposed. It is not only made as an annotated bibliography of past works. It also emphasizes simple basic ideas that govern most of the existing methods, especially the principle of minimum specificify and the combination/projection principle that facilitate a comparison between fuzzy set-based methods and other numerical approaches to automated reasoning. Also, a significant part of the text is devoted to the representation of truth-qualified, certainty-qualified and possibility-qualified fuzzy statements. A new attempt to classify the numerous models of fuzzy “if … then” rules from a semantic point of view is presented. In the past, people have classified them according to algebraic properties of the underlying implication, or by putting constraints on the expected behavior of the inference process (by analogy with classical logic), or by running extensive comparative trials of particular implications on test-examples. Here the classification is based on whether the rules qualify the truth, the certainty or the possibility of their conclusions. Each case corresponds to a specific way of deriving the underlying conditional possibility distribution. This paper focuses on semantic approaches to approximate reasoning based on fuzzy sets, commonly exemplified by the generalized modus ponens, but also considers applications to current topics in Artificial Intelligence such as default reasoning and qualitative process modeling. A companion survey paper is devoted to syntax-oriented methods.