Fuzzy orderings in flexible query answering systems

This paper describes the benefits of using fuzzy orderings in flexible query answering systems. We provide a brief overview of those results from the theory of fuzzy orderings that are necessary to couple fuzzy orderings with flexible querying in a meaningful synergistic way. As one case study, we discuss a simple and pragmatic variant of a flexible query answering system – the so-called Vague query system (VQS). The integration of fuzzy orderings into that system is provided in full detail along with examples.This work was supported by the K_plus Competence Center Program which is funded by the Austrian Government, the Province of Upper Austria, and the Chamber of Commerce of Upper Austria.     

Partial ordering in L-underdeterminate sets

The purpose of this paper is to improve results on fuzzy partial orderings obtained by Zadeh in [9]. We overcome the difficulties connected with the axioms of antisymmetry and linearity. Moreover, if the underlying lattice L is a complete residuated lattice, we establish a Szpilrajn theorem, i.e., any (L-fuzzy) partial ordering has a linear extension. In opposition to Zadeh's, our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless. Therefore we first introduce the category LUS (cf. [2]), which can be considered as a mathematical model of fuzzy equality, and subsequently we specify the axioms of (L-fuzzy) partial orderings with respect to the frame given by LUS. The axioms we use clearly display the usefulness of having a Zadeh-like complementation and, as a consequence, the usefulness of a positivistic (and nonintuitionistic) frame of study. An example concerning L°(Rⁿ) which we give clearly shows that the LUS version of the Szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem, but provides us with additional information.     

Well rewrite orderings and well quasi-orderings

This paper studies well (quasi) orderings described as rewrite orderings and proposes a new family of well (quasi) orderings that extends the embedding or divisibility order of G. Higman. For instance, the well (quasi) orderings proposed in this paper may contain pairs of the form f(f(χ)) >f(g(f(χ))). Conditions called basicity and projectivity under which the transitive closure of a well-founded rewrite relation is a well-quasi-ordering are given. A tool based on narrowing is proposed for proving projectivity.     

自适应属性加权2维FCM分割算法

目的 为了提高2维直方图模糊C均值聚类分割算法的抗噪性和普适性,提出了属性加权2维直方图模糊C均值聚类分割新方法。方法 针对2维直方图模糊C均值聚类分割算法存在阈值参数选取不当导致抗噪性能差的不足,将属性加权引入2维直方图模糊C均值聚类并有效解决了每维属性聚类贡献度的问题。结果 本文算法相比2维直方图模糊C均值聚类分割法抗椒盐和高斯噪声性能平均提高了2～3 dB;同时,相比模糊局部C均值聚类分割法抗椒盐噪声性能平均提高了2～3 dB且抗高斯噪声性能稍差大约1 dB,但本文算法相比模糊局部C均值聚类分割法的速度平均提高了大约40倍。结论 实验结果表明,本文算法相比现有2维直方图模糊C均值聚类算法更适合噪声图像分割;同时,相比模糊局部C均值聚类算法更有利于实时性要求较高场合的目标跟踪和识别等需要。同时从大量图像测试得出,本文算法对于一般人工合成图像、智能交通图像及遥感图像等具有普遍适用性。     

Concordance and consensus

This paper deals with the measurement of concordance and the construction of consensus in preference data, either in the form of preference rankings or in the form of response distributions with Likert-items. We propose a set of axioms of concordance in preference orderings and a new class of concordance measures. The measures outperform classic measures like Kendall’s τ and W and Spearman’s ρ in sensitivity and apply to large sets of orderings instead of just to pairs of orderings. For sets of N orderings of n items, we present very efficient and flexible algorithms that have a time complexity of only O(Nn²). Remarkably, the algorithms also allow for fast calculation of all longest common subsequences of the full set of orderings. We experimentally demonstrate the performance of the algorithms. A new and simple measure for assessing concordance on Likert-items is proposed.     

核空间广义均衡模糊C-均值聚类算法

目的 针对现有广义均衡模糊C-均值聚类不收敛问题,提出一种改进广义均衡模糊聚类新算法,并将其推广至再生希尔伯特核空间以便提高该类算法的普适性。方法 在现有广义均衡模糊C-均值聚类目标函数的基础上,利用Schweizer T范数极限表达式的性质构造了新的广义均衡模糊C-均值聚类最优化目标函数,然后采用拉格朗日乘子法获取其迭代求解所对应的隶属度和聚类中心表达式,同时对其聚类中心迭代表达式进行修改并得到一类聚类性能显著改善的修正聚类算法;最后利用非线性函数将数据样本映射至高维特征空间获得核空间广义均衡模糊聚类算法。结果 对Iris标准文本数据聚类和灰度图像分割测试表明,提出的改进广义均衡模模糊聚类新算法及其修正算法具有良好的分类性能,核空间广义均衡模糊聚类算法对比现有融入类间距离的改进模糊C-均值聚类(FCS)算法和改进再生核空间的模糊局部C-均值聚类(KFLICM)算法能将图像分割的误分率降低10%30%。结论 本文算法克服了现有广义均衡模糊C-均值聚类算法的缺陷,同时改善了聚类性能,适合复杂数据聚类分析的需要。     

NEW METHODOLOGY TO FUZZY REASONING FOR RULE-BASED EXPERT SYSTEMS

Abstract

Much knowledge residing in the knowledge base of an expert system involves fuzzy concepts. A powerful expert system must have the capability of fuzzy reasoning. This paper presents a new methodology for dealing with fuzzy reasoning based on the matching function S. The single-input, single-output (SISO) fuzzy reasoning scheme and the multi-input, single-output (MISO) fuzzy reasoning schemes are discussed in detail. The proposed fuzzy reasoning methodology is conceptually clearer than the compositional rule of inference approach. It can provide an useful way for rule-based systems to deal with fuzzy reasoning.     

The Representation of Fuzzy Knowledge

Abstract

A new AI programming language (called FUZZY) is introduced which provides a number of facilities for efficiently representing and manipulating fuzzy knowledge. A fuzzy associative net is maintained by the system, and procedures with associated “procedure demons” may be defined for the control of fuzzy processes. Such standard AI language features as a pattern-directed data access and procedure invocation mechanism and a backtrack control structure are also available.

This paper examines some general techniques for representing fuzzy knowledge in FUZZY, including the use of the associative net for the explicit representation of fuzzy sets and fuzzy relations, and the use of “deduce procedures” to implicitly define fuzzy sets, logical combinations of fuzzy sets, linguistic hedges, and fuzzy algorithms. The role of inference in a fuzzy environment is also discussed, and a technique for computing fuzzy inferences in FUZZY is examined.

The programming language FUZZY is implemented in LISP, and is currently running on a UNIVAC 1110 computer.     

Basic Lul Factorization And Improved Iterative Method With Orderings

Consider the 'basic LUL factorization' of the matrices as the generalization of the LU factorization and the UL factorization, and using this LUL factorization of the matrices, we propose an "improved iterative method" such that the spectral radius of this iterative matrix is equal to zero, and this method converges at most n iterations. Our main concern is the necessary and sufficient conditions that the improved iterative matrix is equal to the iterative matrix of the improved SOR method with orderings. Concerning the tridiagonal matrices and the upper Hessenberg matrices, this method becomes the improved SOR method with orderings, and we give n selections of the multiple relaxation parameters such that the spectral radii of the corresponding improved SOR matrices are 0. We extend these results to a class of $n \times n$ matrices. We also consider the basic LUL factorization and improved iterated method 'corresponding to permutation matrices'.     

ARE FUZZY SYSTEMS UNIVERSAL APPROXIMATORS?

Abstract

This paper is a critical reflection on various results in lileralure claiming that fuzzy systems are universal approximators. For this purpose the most specific features of fuzzy systems are outlined and it is discussed to which extent they are incorporated in the formal definition of a Tuzzy system in literature. It is argued that fuzzy systems can only be universal approximators in a rather reduced sense where some crucial features are neglected. The goal is to give an impulse to investigate more adequate mathematical concepts of a fuzzy system thai also take into account such features as transparency and linguistic interpretability.     

A Note on the Simplification of Fuzzy Switching Functions

Abstract

This note is concerned with the modification of the definition of fuzzy consensus. The modified version is used to find the set of all fuzzy prime implicants of a fuzzy switching function as defined in [1]. The fuzzy algebra used to derive these functions satisfies the set of axioms of a distributive lattice with unique identities under the operators of maximum and minimum as described in [5], [4], and [3].     

Stability analysis of fuzzy large-scale systems with time delays in interconnections

The stability problem of fuzzy large-scale systems with time delays in interconnections is considered in this paper. The fuzzy large-scale system consists of J interconnected subsystems, which are represented by Takagi-Sugeno (T-S) fuzzy models. The stability conditions are derived using the Lyapunov-Krasovskii functional approach. This condition is independent of time delay and does not need the solution of a Lyapunov equation or Riccati equation. A stabilization approach for the delayed fuzzy large-scale systems through fuzzy state feedback-based controller is also presented in this paper. Finally, an example is given to demonstrate the result.     

模糊熵的区域合并和图割的快速矿岩分割

目的 针对现有区域合并和图割的结合算法没有考虑矿岩图像模糊特性,导致分割精度和运行效率较低,模糊边缘无法有效分割的问题,利用快速递推计算的最大模糊2-划熵信息设置以区域为顶点的图割模型似然能来解决。方法 首先利用双边滤波器和分水岭算法对矿岩图像进行预处理,并将其划分为若干一致性较好的区域;然后利用图像在计算最大模糊2-划分熵时,目标和背景的模糊隶属度函数来设计图割能量函数似然能,使得能量函数更接近模糊图像的真实情况,期间为了提高最大模糊2-划分熵值的搜索效率,提出了时间复杂度为O（n²）的递推算法将模糊熵的计算转化为递推过程,并保留不重复的递推结果用于后续的穷举搜索;最后利用设计的图割算法对区域进行标号,以完成分割。结果 本文算法的分割精度较其他区域合并和图割结合算法提高了约23%,分割后矿岩颗粒个数的统计结果相对于人工统计结果,其误差率约为2%,运行时间较其他算法缩短了约60%。结论 本文算法确保精度同时,有效提高矿岩图像的分割效率,为自动化矿岩图像高效分割的工程实践提供重要指导依据。     

MEMBERSHIP IN A COMPOUND FUZZY SUBSET

Abstract

We first provide a new formulation for a fuzzy subset as a joint relation of the variables, the element and the membership grade of the element. This relationship is developed by appreciating the fact that a fuzzy subset, as is any set, is a union of the elements which constitute it. With a compound fuzzy subset of X defined as a fuzzy subset defined over a base set whose elements are fuzzy subsets of X we suggest a method for obtaining the membership grade of the elements of X in this compound fuzzy subset. This method uses the formulation suggested at the beginning.     

Divergence control for distributed database systems

This paper presents distributed divergence control algorithms for epsilon serializability for both homogeneous and heterogeneous distributed databases. Epsilon serializability allows for more concurrency by permitting non-serializable interleavings of database operations among epsilon transactions. We first present a strict 2-phase locking divergence control algorithm and an optimistic divergence control algorithm for a homogeneous distributed database system, where the local orderings of all the sub-transactions of a distributed epsilon transaction are the same. In such an environment, the total inconsistency of a distributed epsilon transaction is simply the sum of those of all its sub-transactions. We then describe a divergence control algorithm for a heterogeneous distributed database system, where the local orderings of all the sub-transactions of a distributed epsilon transaction may not be the same and the total inconsistency of a distributed epsilon transaction may be greater than the sum of those of all its sub-transactions. As a result, in addition to executing a local divergence control algorithm in each site to maintain the local inconsistency, a global mechanism is needed to take into account the additional inconsistency Recommended by: Meichum Hsu     

Abc classification with uncertain data. a fuzzy model vs. a probabilistic model

This study presents an alternative way of classifying the different productive items of a company. A fuzzy model for the magnitudes involved (demand and cost) is described. This model contrasts with the classic Pareto classification (ABC), which ranks productive items according to their importance in terms of frequency and costs. Whereas rankings obtained using the classical method are based on information about costs and demand over a period in the past, this new method allows new fuzzy information about the future to be included, thus allowing stricter control of the fuzzy ''A-items'' that result from this new classification. Rankings comparing a probabilistic model and its fuzzy counterpart are also provided in this study.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Fuzzy forecasting based on fuzzy time series

This article presents an improved method of fuzzy time series to forecast university enrollments. The historical enrollment data of the University of Alabama were first adopted by Song and Chissom (Song, Q. and Chissom, B. S. (1993). Forecasting enrollment with fuzzy time series-part I, Fuzzy Sets and Systems, 54, 1–9; Song, Q. and Chissom, B. S. (1994). Forecasting enrollment with fuzzy time series-part II, Fuzzy Sets and Systems, 54, 267–277) to illustrate the forecasting process of the fuzzy time series. Later, Chen proposed a simpler method. In this article, we show that our method is as simple as Chen's method but more accurate. In forecasting the enrollment of the University of Alabama, the root mean square percentage error (RMSPE) of our method is 3.1113% while the RMSPE of Chen's method is 4.0516%, which shows that our method is doing much better.     

ON FUZZY INTERPOLATION*

Abstract

This note intends to discuss several connections between interpolative reasoning and fuzzy sets and the role played by the extension principle in this connection. It is first recalled how gradual rules can encode linear or non-linear interpolation between precisely known points and can exactly reconstruct any single-input monotonic real function when the membership functions of the fuzzy sets involved in the rules are suitably chosen. Then linear interpolation between fuzzy points is investigated. The interest of gradual rules as opposed to other approximation schemes is singled out.     

Efficient verification of timed automata with BDD-like data structures

We investigate the effect on efficiency of various design issues for BDD-like data structures of TA state space representation and manipulation. We find that the efficiency is highly sensitive to decision atom design and canonical form definition. We explore the two issues in detail and propose to use CRD (Clock-Restriction Diagram) for TA state space representation and present algorithms for manipulating CRD in the verification of TAs. We compare three canonical forms for zones, develop a procedure for quick zone-containment detection, and present algorithms for verification with backward reachability analysis. Three possible evaluation orderings are also considered and discussed. We implement our idea in our tool Red 4.2 and carry out experiments to compare with other tools and various strategies of Red in both forward and backward analysis. Finally, we discuss the possibility of future improvement.