模糊控制的模糊推理分析

分析了使用RZ算子时推理合成规则(CRI)不具有还原性和不能正确进行模糊推理的原因,给出了正确应用CRI的条件;分析了全蕴涵3I算法的不足及其具有还原性的原因;对各种蕴涵算子的模糊推理进行分析比较,得到了正确的推理算法;对模糊推理在理论和实际应用中的矛盾作了具体说明.     

具有还原性的多重多维模糊推理算法

Zadeh提出的CRI算法是模糊推理中运用最广泛的算法,但它不具还原性。王国俊教授提出的全蕴涵三Ⅰ算法,以及已有的基于相似度的模糊推理算法是在单一规则下的模糊推理算法,在单一规则情形满足还原性条件。本文在给出多重多维模糊推理具有还原性的定义的基础上,先用例子说明,全蕴涵三Ⅰ算法和已有的基于相似度的算法在多重多维推理的情况下不具有还原性,同时本文提出一种新的基于相似度的模糊推理算法,在多重多维推理时满足还原性条件。     

剩余型直觉模糊推理的反向三I方法

提出直觉模糊取式(IFMP)和直觉模糊拒取式(IFMT)问题的直觉模糊推理的反向三I原则、反向α-三I原则和反向三I约束原则.针对剩余型直觉模糊蕴涵算子,给出IFMP、IFMT问题的直觉模糊推理的反向三I算法、反向α-三I算法及反向三I约束算法求解的计算公式和分解形式,指出这些算法都是相应模糊集情形下的推广,讨论IFMP、IFMT问题的直觉模糊推理的反向三I算法的还原性.     

两类模糊推理算法的连续性和逼近性

对Zadeh的模糊推理合成法则(CRI算法)和全蕴涵三I算法(三I算法)是否满足连续性和逼近性问题进行了细致的研究,进一步讨论了这两类算法对逼近误差的传播性能.为此,把模糊推理算法看成是模糊集合到模糊集合的映射,选用海明距离作为两模糊集的距离.证明了在模糊假言推理和模糊拒取式推理情形,这两类算法都拥有连续性.指出三I算法在已知规则的前件和后件是正规集的条件下总是满足逼近性,而CRI算法只有当它满足还原性时才拥有逼近性.在满足逼近性的条件下,两类算法都不会放大逼近误差.结果对构建模糊控制系统和模糊专家系统时选用和分析模糊推理算法有一定的指导作用.     

蕴涵算子族Rλ-L∏GN及其三I支持算法

给出了一族新的伪三角模族Tλ-L∏GN及其伴随蕴涵算子族Rλ-L∏GN,它包括Lukasiewicz蕴涵算子、Gǒdel蕴涵算子、R0蕴涵算子及RΠ蕴涵算子;提出了基于蕴涵算子族的模糊推理的思想,并给出了基于蕴涵算子族Rλ-L∏GN的FMP模型的三I支持算法和α-三I支持算法。     

模糊推理SIS算法的统一形式及其还原性

模糊推理是模糊控制的核心问题,还原性则是评价模糊推理算法好坏的重要标准之一。在正则蕴涵算子的统一框架下,给出了基于模糊推理SIS(subsethood infer subsethood)算法的模糊取式(fuzzy modus ponens,FMP)问题解的统一表达式;基于SIS算法为模糊拒取式(fuzzy modus tollens,FMT)问题提出了一种改进的求解原则,并给出了FMT问题解的统一形式;证明了SIS FMP算法和SIS FMT算法均满足无条件还原性,讨论了FMP问题及FMT问题基于SIS算法的λ-水平解。该算法将为模糊控制领域提供更多可供选择的模糊推理方法。     

基于蕴涵算子族的模糊推理的FMP三I约束算法

提出了基于蕴涵算子族L-λ-R0的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R0给出了模糊推理的FMP模型的α-三I约束算法、三I约束算法,并说明其现实意义。     

基于含参数蕴涵算子族L-λ-R_0的三I支持算法——仅就FMP模型进行讨论

提出了基于蕴涵算子族L-λ-R0的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R0给出了模糊推理的FMP模型的三I支持算法、α-三I支持算法。     

蕴涵算子族G-λ-∏的模糊推理三I支持算法

提出了基于蕴涵算子族G-λ-∏的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族G-λ-∏给出了模糊推理的FMP模型及FMT模型的三I支持算法、α-三I支持算法。     

蕴涵算子族R(q,p)-LGN及其三I支持算法

给出了一族新的左连续三角模族T(q,p)-LGN族及其伴随蕴涵算子族R(q,p)-LGN,它包括Lukasiewicz蕴涵算子、Godel蕴涵算子及R0 蕴涵算子;提出了基于蕴涵算子族的模糊推理的思想,并给出了基于蕴涵算子族R(q,p)-LGN的FMP模型的三I支持算法.     

Probability representations of fuzzy systems

1 Background of birth of fuzzy systems As is well-known, just considering the great uncertainties of many systems, Zadeh put forward the notion of fuzzy sets and advanced the idea of the fuzzy reasoning by means of fuzzy sets which could describe a system approximately[1]. Those systems that are constructed on the basis of fuzzy reasoning are called fuzzy systems in general[2―4]. The research on fuzzy systems has attracted broad attention[5―7]. For instance, universal ap- proximation proper…     

Truth-value transmittal fuzzy reasoning interpolator

Fuzzy reasoning and interpolation were used independently as two methods of ex- pression functional relationship approximately in the past. The relevancy behind them was discussed firstly in refs. [1―3]. In ref. [1], fuzzy reasoning algorithms used com- monly at present were approximated to some interpolation algorithms. Based on the analysis of rationality of such approximation, the author of ref. [4] put forward the con- cept of the fuzzy reasoning interpolator. In this paper, we keep on re…     

Unified forms of Triple I method

First, the present paper provides unified forms of Triple I method for fuzzy modus ponens and fuzzy modus tollens of which diverse implication operators can be employed. Second, it is clarified that, in a sense, Zadeh's CRI method for fuzzy modus ponens can be brought into line with the unified form of the Triple I method. Lastly, a unified form of α-Triple I method is established as well, and a duality result concerning α-Triple I solutions of fuzzy modus ponens and fuzzy modus tollens is obtained.     

解释模型类理论及其极小三I-算法

首先在多类（many-sorted）一阶形式系统Lukms、Gödms,∏ms和L^*ms中通过引入多类一阶模糊语言Lms的解释模型类及基于解释模型类的α-逻辑有效公式的概念,建立了多类一阶模糊语言的解释模型类理论;然后,基于上述理论探讨了模糊推理算法（CRI及三I算法）与其理论Г-推理的关系,从而进一步奠定了模糊推理的理论基础,同时得到一种新型的模糊推理算法,称为极小三I算法。     

基于蕴涵算子族L-λ-R_0的FMT三Ⅰ约束算法

提出了基于蕴涵算子族L-λ-R0的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R0给出了FMT模型的三I约束算法、α-三I约束算法。给出了FMT模型的三I约束算法、α-三I约束算法计算公式。     

A comparative study on similarity-based fuzzy reasoning methods

If the given fact for an antecedent in a fuzzy production rule (FPR) does not match exactly with the antecedent of the rule, the consequent can still be drawn by technique such as fuzzy reasoning. Many existing fuzzy reasoning methods are based on Zadeh's Compositional Rule of Inference (CRI) which requires setting up a fuzzy relation between the antecedent and the consequent part. There are some other fuzzy reasoning methods which do not use Zadeh's CRI. Among them, the similarity-based fuzzy reasoning methods, which make use of the degree of similarity between a given fact and the antecedent of the rule to draw the conclusion, are well known. In this paper, six similarity-based fuzzy reasoning methods are compared and analyzed. Two of them are newly proposed by the authors. The comparisons are two-fold. One is to compare the six reasoning methods in drawing appropriate conclusions for a given set of FPRs. The other is to compare them based on five issues: 1) types of FPR handled by these methods; 2) the complexity of the methods; 3) the accuracy of the conclusion drawn; 4) the accuracy of the similarity measure; and 5) the multi-level reasoning capability. The results have shed some lights on how to select an appropriate fuzzy reasoning method under different environments.     

基于蕴涵算子族Lλ0λG的模糊推理三I约束算法

提出了基于蕴涵算子族Lλ0λG的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族Lλ0λG给出了模糊推理的FMP模型及FMT模型的三I约束算法。     

基于蕴涵算子族L-λ-R0的FMT三I约束算法

提出了基于蕴涵算子族L-λ-R₀的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R₀给出了FMT模型的三I约束算法、α-三I约束算法。给出了FMT模型的三I约束算法、α-三I约束算法计算公式。     

Vague集上的快速CRI方法

CRI方法是模糊推理的重要方法之一,然而常用的CRI方法的时间和空间复杂度均为O(mn)。相对于Fuzzy集而言,Vague集所能表达的信息更加丰富,更接近实际。故首先把Fuzzy集上的CRI方法和max-min算子扩充到Vague集上,得到基于Vague集的CRI方法。为了降低CRI方法的时间复杂度,深入分析了max-min算子相关性质,最后得到一个快速的CRI方法,其时间复杂度和空间复杂度降为O(m+n)。最后用实例来说明该方法的高效性。