正则半群上模糊同余的模糊核

模糊核迹方法是研究正则半群上模糊同余的重要手段，模糊核作为一个方法的组成部分成为重要的讨论对象。目的在于研究正则半群的模糊子集满足什么条件构成模糊同余的模糊核：引入一般半群上的模糊等价关系浸满一个模糊子集的概念，证明了正则半群上每个模糊同余浸满它的模糊核，给出了正则半群的模糊子集是某个模糊同余的模糊核的充要条件。     

模糊强半预开集和模糊强半预连续性(英文)

本文引入并讨论模糊拓扑空间中的模糊强半预开集和模糊强半预连续映射及其基本性质     

Fuzzy risk matrix

A risk matrix is a mechanism to characterize and rank process risks that are typically identified through one or more multifunctional reviews (e.g., process hazard analysis, audits, or incident investigation). This paper describes a procedure for developing a fuzzy risk matrix that may be used for emerging fuzzy logic applications in different safety analyses (e.g., LOPA). The fuzzification of frequency and severity of the consequences of the incident scenario are described which are basic inputs for fuzzy risk matrix. Subsequently using different design of risk matrix, fuzzy rules are established enabling the development of fuzzy risk matrices. Three types of fuzzy risk matrix have been developed (low-cost, standard, and high-cost), and using a distillation column case study, the effect of the design on final defuzzified risk index is demonstrated.     

带有饱和执行器的T-S模糊时滞系统的模糊控制

研究了带有饱和执行器及时变时滞的T-S模糊系统的控制律设计问题.利用PDC技术、Razumikhin稳定性理论以及线性矩阵不等式(LMI)方法,建立了闭环模糊系统渐近稳定的时滞依赖的判别条件,给出了模糊控制律的设计方法.通过求解LMI,可以获得闭环模糊系统的吸引域的估计.最后,提出了闭环系统吸引域的估计最大化的模糊控制律的一个设计方法.     

Fuzzy set theory

Zusammenfassung Seit Beginn der neunziger Jahre wird unter dem Schlagwort Fuzzy Logic von einer Vielzahl von Anwendungen der Theorie unscharfer Mengen vor allem in Japan berichtet. Dies hat in Europa und hier insbesondere in Deutschland zu einem Umdenken bei Wissenschaftlern und Praktikern geführt, die lange Zeit die Potentiale der neuen Technologie verkannten. Nun ist schlagartig eine sehr große Nachfrage nach Informationen zu diesem Thema entstanden. Dieser Artikel gibt einen Überblick über die wesentlichen Grundlagen der Theorie unscharfer Mengen und zeigt potentielle Anwendungen auf.     

A Development of Fuzzy Encoding and Decoding Through Fuzzy Clustering

Fuzzy clustering has emerged as a fundamental technique of information granulation. In this study, we introduce and discuss multivariable encoding and decoding mechanisms (referred altogether as a reconstruction problem) expressed in the language of fuzzy sets and fuzzy relations. The underlying performance index associated with the problem helps quantify a reconstruction error that arises when transforming a numeric datum through fuzzy sets (relations) and then reconstructing it into an original numeric format. The clustering platform considered in this study concerns the well-known algorithm of Fuzzy C-Means (FCM). The main design aspects deal with the relationships between the number of clusters versus the reconstruction properties and the resulting reconstruction error. The impact of the fuzzification coefficient on the reconstruction quality is investigated. This finding is of interest, given the fact that predominantly all applications involving FCM use the value of the fuzzification coefficient equal to 2. In light of the completed experiments, we demonstrate that this selection may not be experimentally legitimate. We also carry out a comparative analysis of the reconstruction properties of the Boolean decoding that is induced by the fuzzy partition. Experimental investigations involve selected machine learning data.     

模糊拟阵研究

李传东等人研究了模糊子拟阵,然而,这些工作是在作者误认为模糊拟阵和次模糊拟阵等价的前提下做出的.本文首先给出两个例子说明模糊拟阵和次模糊拟阵是两个不同的概念.其次,把分明拟阵中的限制,截短等运算推广到模糊拟阵中,并且定义了模糊拟阵的垂直截短、水平截短、水平限制等运算.最后证明了模糊拟阵的基本列包含其水平限制的基本列.     

模糊聚类分析在模糊神经网络结构优化中的应用

研究了模糊聚类分析在多变量模糊神经网络的结构确定中的应用,在传统的模糊C－均值算法的基础上,给出了一个衡量聚类有效性的函数和确定模糊指数的启发式方法,并给出了应用该算法的具体的模糊神经网络模型。     

模糊关系方程的解的模糊遗传寻优算法

在一般遗传算法ＧＡ的基础上，基于模糊集理论中的模糊关系方程的解的寻优问题提出了模糊遗传算法ＦＧＡ，它能有效地找出模糊关系方程的解的寻优问题的近似最优解。还给出了一个重要的定理：模糊模式定理。     

带有积压定单的最优模糊存储模型

本文提出一个新的具有积压定单的关于模糊总需求的模糊存储模型。在模糊函数原理下，给出了模糊总存储成本。为了寻找最优解，使用积分均值法白化模糊总存储成本，利用Lingo8．0求解不等式约束问题，我们发现最优解都是确定的实数。此外，当模糊总需求是确定的实数时，我们提出模型的最优解与经典的具有积压定单存储模型具有相同的结果。     

Multimodal Fuzzy Downstream Petroleum Supply Chain: A Novel Pentagonal Fuzzy Optimization

The petroleum industry has a complex, inflexible and challenging supply chain (SC) that impacts both the national economy as well as people’s daily lives with a range of services, including transportation, heating, electricity, lubricants, as well as chemicals and petrochemicals. In the petroleum industry, supply chain management presents several challenges, especially in the logistics sector, that are not found in other industries. In addition, logistical challenges contribute significantly to the cost of oil. Uncertainty regarding customer demand and supply significantly affects SC networks. Hence, SC flexibility can be maintained by addressing uncertainty. On the other hand, in the real world, decision-making challenges are often ambiguous or vague. In some cases, measurements are incorrect owing to measurement errors, instrument faults, etc., which lead to a pentagonal fuzzy number (PFN) which is the extension of a fuzzy number. Therefore, it is necessary to develop quantitative models to optimize logistics operations and supply chain networks. This study proposed a linear programming model under an uncertain environment. The model minimizes the cost along the refineries, depots, multimode transport and demand nodes. Further developed pentagonal fuzzy optimization, an alternative approach is developed to solve the downstream supply chain using the mixed-integer linear programming (MILP) model to obtain a feasible solution to the fuzzy transportation cost problem. In this model, the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number. Furthermore, defuzzification is performed using an accuracy function. To validate the model and technique and feasibility solution, an illustrative example of the oil and gas SC is considered, providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.     

Fuzzy Time-Driven Activity-Based Costing

Abstract:

Activity-Based Costing (ABC) method is a well-known costing/accounting system. It is an alternative to traditional accounting systems in which business overheads are allocated in proportion to activity's direct costs. Kaplan and Anderson proposed the second generation of the ABC system, called “time-driven activity-based costing” (TDABC), which seeks to resolve some of its drawbacks. The TDABC approach is mainly based on the time drivers spent on cost pools; however, TDABC poses some difficulties in calculations of the assigned costs. Unavailability of accurate and reliable time drivers, variety of time drivers, difficulties of collecting and updating data through calculation procedure, and huge volume of data are some examples of the difficulties. In this article, via utilizing the triangular fuzzy number (TFN), a novel mechanism for the TDABC system is proposed. We employ fuzzy logic to estimate inputs required for TDABC, namely, the required time to perform each activity and practical capacity. Our proposed approach highlights deviations caused by deterministic estimates in TDBAC and makes our estimates more realistic. In addition, sensitivity analysis can be conducted with our proposed approach. Finally, all plausible conditions ranging from the worst case to the best case can be considered; therefore, insightful and appropriate managerial decisions can be made.     

Discussion: Fuzzy Thinking

This article investigates computation of pointwise and simultaneous tolerance limits under the logistic regression model for binary data. The data consist of n binary responses, where the probability of a positive response depends on covariates via the logistic regression function. Upper tolerance limits are constructed for the number of positive responses in m future trials for fixed as well as varying levels of the covariates. The former provides pointwise upper tolerance limits, and the latter provides simultaneous upper tolerance limits. The upper tolerance limits are obtained from upper confidence limits for the probability of a positive response, modeled using the logistic function. To compute pointwise upper confidence limits for the logistic function, likelihood-based asymptotic methods, small sample asymptotics, as well as bootstrap methods are investigated and numerically compared. To compute simultaneous upper tolerance limits, a bootstrap approach is investigated. The problems have been motivated by an application of interest to the U.S. Army, dealing with the testing of ballistic armor plates for protecting soldiers from projectiles and shrapnel, where the success probability depends on covariates such as the projectile velocity, size of the armor plate, etc. Such an application is used to illustrate the tolerance interval computations in the article. We provide the R codes used for the calculations presented in the examples in the article as supplementary material, available online.     

关于模糊优化设计

<正> 模糊优化设计,是在优化设计中包含有种种模糊因素的设计,是近年来在模糊数学的基础上发展起来的一种新的优化方法,具有广阔的前景。本文对它的基本概念、方法和动态作一简要介绍,抛砖引玉,以引起有关同事注意,共同促进这一工作的研究和发展。     

模糊数学方法在机械设计中的应用

本文应用模糊数学理论,针对模糊设计计算问题,提出了基于模糊数的设计计算方法,并给出了具体的设计计算实例。     

基于模糊因子法的模糊桁架结构动力特性分析

研究了模糊桁架结构动力特性的分析方法,在结构的物理和几何参数同时为模糊变量的情况下,利用模糊因子建立了结构的刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用区间运算法则推导出结构模糊特征值的表达式。通过算例考察了结构各参数的模糊性对其动力特性模糊性的影响,并获得了一些有意义的结论。该法对模糊结构进行一次动力分析便可求得动力特性,且可充分地反映任一模糊参数对结构模糊动力特性的影响。     

Fuzzy rule-based image processing

A novel image-processing technique based on fuzzy rules is proposed. This technique uses human knowledge about how an image should be processed depending on the local characteristics of image. The knowledge is represented by fuzzy rules and is also represented by a multidimensional nonlinear function which can be optimized by training. Efficient noise reduction and edge detection are realized by this fuzzy rule-based method. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 457–461, 1997     

Dynamic Response Analysis of Fuzzy Stochastic Truss Structures under Fuzzy Stochastic Excitation

A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper.     

模糊数据中异常点的一种识别方法

针对输入为确定数、输出为LR型模糊数的模糊数据集,利用最小二乘法建立了该模糊数据集的模糊线性回归分析模型及参数估计,用数据删除的方法研究了数据删除模糊线性回归模型,构造了统计诊断量—模糊Cook距离来识别模糊数据集中的异常点,通过数值模拟和对实例的研究,识别出其异常点,证实了本文构造的统计诊断量的有效性.     

关于模糊逻辑与模糊推理逻辑基础问题的十年研究综述

自从1993年发生关于模糊逻辑的一场争论以来,模糊逻辑和模糊推理研究在十年里得到了迅速的发展。本文对这十年国内外关于模糊逻辑和模糊推理研究的大致情况做一个回顾,简要分析这些研究工作的主要特点。