Design of fuzzy logic controllers based on generalized T-operators

Since Zadeh first proposed the basic principle of fuzzy logic controllers in 1968, the and operators have been popular in the design of fuzzy logic controllers. In this paper, the general concept of T-operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available. Then, by computer simulations, studies are made so as to determine the relations between the various T-operators and the performance of a fuzzy logic controller. It is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the T-operators.     

Exact calculations of extended logical operations on fuzzy truth values

In this paper we propose computationally simple, pointwise formulas for extended t-norms and t-conorms on fuzzy truth values. The complex convolutions of the extended operations are shown to be equivalent to simple pointwise expressions for several special cases. Linear fuzzy truth values are defined and it is shown that the extended Łukasiewicz operations preserve linearity. Since linear fuzzy truth values are common in representing linguistic modifiers, the results simplify fuzzy truth value-based reasoning methods. The results can also be applied immediately to type-2 fuzzy set operations.     

一种基于模糊推理的因素权重确定方法

在模糊综合评价中,如何确定因素的权重是非常重要的,也是非常困难的,它直接关系到评价结果的合理性与真实性.利用模糊推理技术,提出了一种基于模糊推理的因素权重确定方法,其利用人们处理复杂问题的逻辑思维方式,建立评价空间和单位评价空间的映射,得到模糊关系方程并用于确定因素的权重.实验结果表明,利用该模型得到的权重能反映各因素的重要性,用其对待评对象进行模糊综合,其结果也是合理的.     

基于神经网络的模糊推理

为了使模糊推理符合推理原则，目前已定义了１０多种模糊关系，但各种模糊关系定义都存在一定的缺陷。本文提出的基于神经网络的模糊推理，能很好地符合模糊推理原则。     

Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets

Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning.     

模糊推理中的真值传播研究

研究模糊推理的问题,提出了一种真值传播的计算公式与方法,这种算法可以区别精确推理和模糊推理,也可以区别推理条件多与寡的推理。     

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.     

模糊推理全蕴涵算法及其还原性

模糊推理是模糊控制的逻辑基础,然而通用的模糊推理CRI算法却缺乏严格的逻辑依据,近期问世的模糊推理全蕴涵三I算法有效地改进了CRI算法。本文研究了全蕴涵三I算法的一般计算公式及其还原性问题,并且得到了一些新的算法,也提出了一些新的观点,文献中已有的结果大多数是本文结果的特例。从而为模糊推理提供了一种新方法。     

Realization of PID controls by fuzzy control methods

This paper shows that PID controllers can be realized by fuzzy control methods of “product-sum-gravity method” and “simplified fuzzy reasoning method”. PID controllers, however, cannot be constructed by min-max-gravity method known as Mamdani's fuzzy reasoning method. Furthermore, extrapolative reasoning can be executed by the product-sum-gravity method and simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules.     

关于三角模的直觉模糊群及其同态像

本文在K．Atanassov引进的直觉模糊集概念的基础上,利用T模和S模,定义了两个直觉模糊集的乘积．给出了关于三角模的直觉模糊群的概念及其等价命题,最后在两个经典群同态与同构意义下,研究了这种直觉模糊群的同态像及原像等问题。     

基于证据推理的直觉模糊多属性群决策方法

针对属性值为直觉模糊数的多属性群决策问题,提出了一种证据推理的扩展方法。首先,在考虑主观因素与客观因素的基础上运用直觉模糊熵法计算出属性及专家的综合权重。其次,提出一种基于证据推理的直觉模糊信息融合方法,该方法可以避免由于评价值的隶属度为0而导致的信息丢失现象,弥补了现有直觉模糊信息融合方法存在的不足。在此基础上,集结评价信息并按照备选方案与理想方案的相对贴近度对备选方案进行比选。最后,运用实例验证了所提方法的有效性。     

基于可能度的一种直觉模糊集相似度测量方法

研究直觉模糊集的相似度测量方法. 首先给出两个直觉模糊数比较的可能度公式及其性质. 在此基础上, 定义两个直觉模糊集间的相似度测量公式, 分析用此公式进行相似度测量的优缺点, 旨为直觉模糊集在决策、模式识别和医疗诊断中的应用提供更为合理的工具.     

复模糊数及其收敛性

在新的模糊数序关系意义下,将定义在所有实模糊数上的模糊距离推广到所有复模糊数集上的模糊距离.并以此为基础,定义了复模糊数列的极限,讨论了复模糊数列的保号性、有界性等收敛性质及C auchy收敛判别法等.     

Metric properties of the nearest extended parametric fuzzy number and applications

We propose the notion of extended parametric fuzzy number, which generalizes the extended trapezoidal fuzzy number and parametric fuzzy number, discussed in some recent papers. The metric properties of the nearest extended parametric fuzzy number of a fuzzy number, proved in the present article, help us to obtain the property of continuity for the parametric approximation operator and to simplify the solving of the problems of parametric approximations under conditions.     

Bipolar fuzzy relation equations systems based on the product t‐norm

Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation simultaneously can give very useful information for certain frameworks where the human reasoning plays a key role. Hence, the resolution of bipolar fuzzy relation equations systems is a research topic of great interest. This paper focuses on the study of bipolar fuzzy relation equations systems based on the max‐product t‐norm composition. Specifically, the solvability and the algebraic structure of the set of solutions of these bipolar equations systems will be studied, including the case in which such systems are composed of equations whose independent term be equal to 0. As a consequence, this paper complements the contribution carried out by the authors on the solvability of bipolar max‐product fuzzy relation equations.     

区域基础教育信息化水平及课程整合状态的模糊综合评价

以广西区域教育信息化现状调查为基础,对教师、学生的信息化水平进行模糊综合评价并由模糊推理得到信息技术与学科课程整合状态的评价,最后作进一步的分析模型得到整合状态不佳的原因.     

Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations

This paper proposes linear goal programming models for deriving intuitionistic fuzzy weights from intuitionistic fuzzy preference relations. Novel definitions are put forward to define additive consistency and weak transitivity for intuitionistic fuzzy preference relations, followed by a study of their corresponding properties. For any given normalized intuitionistic fuzzy weight vector, a transformation formula is furnished to convert the weights into a consistent intuitionistic fuzzy preference relation. For any intuitionistic fuzzy preference relation, a linear goal programming model is developed to obtain its intuitionistic fuzzy weights by minimizing its deviation from the converted consistent intuitionistic fuzzy preference relation. This approach is then extended to group decision-making situations. Three numerical examples are provided to illustrate the validity and applicability of the proposed models.     

Relating and extending semantical approaches to possibilistic reasoning

Two main semantical approaches to possibilistic reasoning with classical propositions have been proposed in the literature. Namely, Dubois-Prade's approach known as possibilistic logic, whose semantics is based on a preference ordering in the set of possible worlds, and Ruspini's approach that we redefine and call similarity logic, which relies on the notion of similarity or resemblance between worlds. In this article we put into relation both approaches, and it is shown that the monotonic fragment of possibilistic logic can be semantically embedded into similarity logic. Furthermore, to extend possibilistic reasoning to deal with fuzzy propositions, a semantical reasoning framework, called fuzzy truth-valued logic, is also introduced and proved to capture the semantics of both possibilistic and similarity logics.     

Fuzzy reasoning in the investigation of seismic behavior

In this paper, we propose a fuzzy logic–based mathematical model of a sequence of earthquakes using fuzzy reasoning tools. We formed a set of fuzzy implications in order to study them, and we computed their deviation, so that we could compare them and conclude about the most accurate one. The compositional rule of inference was considered, which is based on the generalized modus ponens scheme. The new fuzzy methodology was used for each implication. The data required for the implications were obtained from the aftershocks of an earthquake with significant effects in a specific area. The magnitude of the aftershocks and their time difference from the main incident provided the values for the new fuzzy algorithm application. Two samples were selected relative with the seismic activity, which occurred the following days. The one sample consisted of 30 values, and the other sample from all the values found in the data archives of the National Observatory of Athens. Results were shown for both samples. So a mathematical technique, which reproduces the incidents using basic information and based on only two parameters, is developed for the simulation of a seismic sequence, which follows a strong earthquake.