基于逐点优化模糊推理的模糊控制器及其插值机理

本文从直观优化思想出发,提出一种逐点优化模糊推理方法,称之为POFI方法. 首先分别给出了基于POFI方法的Mamdani蕴涵算子、代数积蕴涵算子和Zadeh蕴涵算子的FMP算法与FMT算法中寻求推理后件(或前件)的计算表达式.然后分别获得了基于POFI方法的Mamdani蕴涵算子模糊控制器、代数积蕴涵算子模糊控制器、Zadeh蕴涵算子模糊控制器及加乘算子模糊控制器的插值表示,由此发现这些模糊控制器具有函数逼近的泛性.其次指出在基于POFI方法的单输入单输出情况下,Mamdani蕴涵算子模糊控制器、代数积蕴涵算子模糊控制器及加乘算子模糊控制器三者相互等效,并且在基于POFI方法的双输入单输出情况下,Mamdani蕴涵算子模糊控制器与代数积蕴涵算子模糊控制器是等效的.     

基于输入-输出数据的概率分布和数字特征

利用模糊推理建立了一种基于输入-输出数据构造联合概率密度函数的方法.首先,将一组单输入-单输出数据转换成模糊推理规则,通过选择适当的模糊蕴涵算子生成模糊关系,再利用这种模糊关系求出二维随机变量的联合概率密度函数.当将模糊蕴涵分别取为Larsen蕴涵和Mamdani蕴涵时,分别得到了两种具体的概率密度函数(称之为Lars...     

基于Mamdani型模糊推理的震中烈度预测模型

对应用模糊推理进行系统预测进行了深入的研究,建立了以震级和震源深度为输入的基于Mamdani型模糊推理的震中烈度预测模型.并以四川地区震例数据为例,对数据信息提取,模糊规则建立等关键环节进行了详细的介绍,预测结果分析表明推理模型是可行和有效的.     

基于输入-输出数据的重心法模糊系统及其泛逼近性

研究基于输入-输出数据的重心法模糊系统及其泛逼近性.首先,将一组单输入-单榆出数据转换成模糊推理规则,通过选择适当的模糊蕴涵算子生成模糊关系,再利用这种模糊关系求出二雄随机变量的联合概率密度函数.当将模糊蕴涵分别取为Larsen蕴涵和Mamdani蕴涵时,分别得到了两种具体的概率密度函数(称之为Larsen分布和Mamdani分布).其次,利用这两种概率分布.分别求出了对应的两种回归函数,指出这种回归函数实际上是模糊控制中的重心法模糊系统.我们分别给出了这种模糊系统具有泛逼近性的充分条件.从而进一步揭示了模糊系统的概率论意义.     

About premise reduction of fuzzy inference algorithm

The comprehensive model with “weighted-objective nearness degree” is introduced in the process of multi-objective decision-making, by which a reduction problem of inference antecedents is studied in traditional fuzzy inference method. Moreover, based on the comprehensive model with “weighted-objective nearness degree”, SMTT fuzzy inference algorithm is proposed. This algorithm not only shows the relative importance of every antecedent component in fuzzy inference, but also considers the influence of nearness degree between every antecedent component’s evaluation and inference objective on inference conclusions. The enactment of inference objective reflects the preference degree of decision maker to every antecedent component’s evaluation. Therefore, it is much fitter for the demands of practical inference.     

A way to deal with fuzzy preferences in multi-criteria decision problems

This paper presents a special multiple criteria decision making approach for solving problems in context with fuzzy individual preferences.At first we briefly expose the proposed methodology. The individual preferences are explicitly given by a complete transitive relation R on a set of reference actions. The modelling of the decision-maker's preferences is obtained by means of fuzzy outranking relations. These fuzzy relations are based on a system of additive utility functions which are estimated by means of ordinal regression methods analysing the preference relation R.This is followed by a presentation of two real multicriteria problems which the proposed methodology has been applied to, i.e. a highway plan choice problem and a problem in marketing research dealing with the launching of a new product. In each application we tried to specify this method according to the specific structure of the problem considered.     

Fuzzy inference to assess manufacturing process capability with imprecise data

Process capability indices provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The loss-based process capability index C_pm, sometimes called the Taguchi index, was proposed to measure process capability, wherein the output process measurements are precise. In the present study, we develop a realistic approach that allows the consideration of imprecise output data resulting from the measurements of the products quality. A general method combining the vector of fuzzy numbers to produce the membership function of fuzzy estimator of Taguchi index is introduced for further testing process capability. With the sampling distribution for the precise estimation of C_pm, two useful fuzzy inference criteria, the critical value and the fuzzy P-value, are proposed to assess the manufacturing process capability based on C_pm. The presented methodology takes into the consideration of a certain degree of imprecision on the sample data and leads to the three-decision rule with the four quadrants decision-making plot. The fuzzy inference procedure presented to assess process capability is a natural generalization of the traditional test, when the data are precise the proposed test is reduced to a classical test with a binary decision.     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

A survey of fuzzy decision tree classifier

Decision-tree algorithm provides one of the most popular methodologies for symbolic knowledge acquisition. The resulting knowledge, a symbolic decision tree along with a simple inference mechanism, has been praised for comprehensibility. The most comprehensible decision trees have been designed for perfect symbolic data. Over the years, additional methodologies have been investigated and proposed to deal with continuous or multi-valued data, and with missing or noisy features. Recently, with the growing popularity of fuzzy representation, some researchers have proposed to utilize fuzzy representation in decision trees to deal with similar situations. This paper presents a survey of current methods for Fuzzy Decision Tree (FDT) designment and the various existing issues. After considering potential advantages of FDT classifiers over traditional decision tree classifiers, we discuss the subjects of FDT including attribute selection criteria, inference for decision assignment and stopping criteria. To be best of our knowledge, this is the first overview of fuzzy decision tree classifier.     

Symmetric implicational method of fuzzy reasoning

Fuzzy reasoning should take into account the factors of both the logic system and the reasoning model, thus a new fuzzy reasoning method called the symmetric implicational method is proposed, which contains the full implication inference method as its particular case. The previous full implication inference principles are improved, and unified forms of the new method are respectively established for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) to let different fuzzy implications be used under the same way. Furthermore, reversibility properties of the new method are analyzed from some conditions that many fuzzy implications satisfy, and it is found that its reversibility properties seem fine. Lastly, the more general α-symmetric implicational method is put forward, and its unified forms are achieved.     

Some considerations on fuzzy conditional inference

In much of human reasoning, the form of reasoning is approximate rather than exact as in ‘A red apple is ripe and this apple is more or less red. Then this apple is more or less ripe.’L.A. Zadeh and E.H. Mamdani suggested methods for such a fuzzy reasoning as an application of fuzzy set theory. The method involves an inference rule and a conditional proposition which contains fuzzy concepts.In this paper we point out that the consequence inferred by their methods does not always fit our intuitions and we suggest the improved methods which fit our intuitions under several criteria.     

Multiple agents finitely repeated inspection game with dismissals

Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpose is to assist them in the task of selecting project portfolios. We have approached this problem by proposing a general nonlinear binary multi-objective mathematical model, which takes into account all the most important factors mentioned in the literature related with Project Portfolio Selection and Scheduling. Due to the existence of uncertainty in different aspects involved in the aforementioned decision task, we have also incorporated into the model some fuzzy parameters, which allow us to represent information not fully known by the decision maker/s. The resulting problem is both fuzzy and multiobjective. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision maker/s.     

一类模糊逻辑系统幺半群与同态映射

首先利用代数中幺半群的概念给出了模糊逻辑系统专业领域的概念, 建立专业领域概念的目的是为了规范模糊逻辑系统中语言变量的取值范围, 从而将模糊逻辑系统看作是某个笛卡儿乘积幺半群的有限子集. 然后利用这个笛卡儿乘积幺半群的乘积运算构造了模糊逻辑系统幺半群. 最后, 在一定的约定条件下证明了通常使用的一类Mamdani形模糊逻辑系统的输出可以看作是从模糊逻辑系统幺半群到连续函数域的同态映射.     

一种区间Pythagorean模糊VIKOR多属性群决策方法

针对属性信息为区间Pythagorean模糊集且属性权重和专家权重均未知的一类群决策问题, 结合信息熵理论, 提出了一种区间Pythagorean模糊VIKOR多属性群决策方法。首先定义一种新的区间Pythagorean模糊距离测度, 并讨论其性质。其次基于该距离测度定义了区间Pythagorean模糊相对距离指数, 并基于相对距离指数构建了一种熵权模型确定专家权重和属性权重。然后提出一种区间Pythagorean模糊VIKOR多属性群决策方法。最后通过企业生产方案选择案例说明了提出新方法的可行性与有效性。     

Fuzzy graphs modelling for HazMat telegeomonitoring

Telegeomonitoring system development combines two heterogeneous technologies: the geographical information systems technology (GIS) and telecommunications technology. In this paper, we give the system components for telegeomonitoring transportation of hazardous materials. The telegeomonitoring system uses GIS to capture civil infrastructure (urban network, land use, industries, etc.) and decision support systems technology to allow risks analysis and evaluate routing strategies that minimize transportation risk. Routing algorithms are to this effect adapted to graphs of the fuzzy risk. A new algebraic structure is proposed to solve a path-finding problem in a fuzzy graph. This algebraic structure is adapted precisely to solve the problem of the K-best fuzzy shortest paths. The approach that we proposed, consists of defining generic structures of operator’s traversal problem in fuzzy graphs. The principal contribution of our approach is to build adequate structures of path algebra to solve the problem of graph traversal in a fuzzy graph without negative circuits. Foundations of the system studied in this work will be able to be transposed to other fields of transportation.     

Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method

This paper proposes a mathematical programming method to construct the membership functions of the fuzzy objective value of the cost-based queueing decision problem with the cost coefficients and the arrival rate being fuzzy numbers. On the basis of Zadeh’s extension principle, three pairs of mixed integer nonlinear programs (MINLP) parameterized by the possibility level α are formulated to calculate the lower and upper bounds of the minimal expected total cost per unit time at α, through which the membership function of the minimal expected total cost per unit time of the fuzzy objective value is constructed. To provide a suitable optimal service rate for designing queueing systems, the Yager’s ranking index method is adopted. Two numerical examples are solved successfully to demonstrate the validity of the proposed method. Since the objective value is completely expressed by a membership function rather than by a crisp value, it conserves the fuzziness of the input information, thus more information is provided for designing queueing systems. The successful extension of queueing decision models to fuzzy environments permits queueing decision models to have wider applications in practice.     

Solving the multiobjective possibilistic linear programming problem

In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM), who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets for which a lot of fuzzy approaches to multiobjective programming have been developed. In this paper we propose a method to solve a multiobjective linear programming problem involving fuzzy parameters (FP-MOLP), whose possibility distributions are given by fuzzy numbers, estimated from the information provided by the DM. As the parameters, intervening in the model, are fuzzy the solutions will be also fuzzy. We propose a new Pareto Optimal Solution concept for fuzzy multiobjective programming problems. It is based on the extension principle and the joint possibility distribution of the fuzzy parameters of the problem. The method relies on α-cuts of the fuzzy solution to generate its possibility distributions. These ideas are illustrated with a numerical example.     

On Compatibility of Interval Fuzzy Preference Relations

This paper defines the concept of compatibility degree of two interval fuzzy preference relations, and gives a compatibility index of two interval fuzzy preference relations. It is proven that an interval fuzzy preference relation B and the synthetic interval fuzzy preference relation of interval fuzzy preference relations A ₁,A ₂,...,A _s are of acceptable compatibility under the condition that the interval fuzzy preference relation B and each of the interval fuzzy preference relations A _l,A ₂,...,A _s are of acceptable compatibility, and thus a theoretic basis has been developed for the application of the interval fuzzy preference relations in group decision making.     

Self-tuning of fuzzy belief rule bases for engineering system safety analysis

A framework for modelling the safety of an engineering system using a fuzzy rule-based evidential reasoning (FURBER) approach has been recently proposed, where a fuzzy rule-base designed on the basis of a belief structure (called a belief rule base) forms a basis in the inference mechanism of FURBER. However, it is difficult to accurately determine the parameters of a fuzzy belief rule base (FBRB) entirely subjectively, in particular for complex systems. As such, there is a need to develop a supporting mechanism that can be used to train in a locally optimal way a FBRB initially built using expert knowledge. In this paper, the methods for self-tuning a FBRB for engineering system safety analysis are investigated on the basis of a previous study. The method consists of a number of single and multiple objective nonlinear optimization models. The above framework is applied to model the system safety of a marine engineering system and the case study is used to demonstrate how the methods can be implemented.