Showing papers on "Fuzzy associative matrix published in 2004"

Fuzzy expert systems and fuzzy reasoning

Abstract: Preface. 1 Introduction. 1.1 Characteristics of Expert Systems. 1.2 Neural Nets. 1.3 Symbolic Reasoning. 1.4 Developing a Rule-Based Expert System. 1.5 Fuzzy Rule-Based Systems. 1.6 Problems in Learning How to Construct Fuzzy Expert Systems. 1.7 Tools for Learning How to Construct Fuzzy Expert Systems. 1.8 Auxiliary Reading. 1.9 Summary. 1.10 Questions. 2 Rule-Based Systems: Overview. 2.1 Expert Knowledge: Rules and Data. 2.2 Rule Antecedent and Consequent. 2.3 Data-Driven Systems. 2.4 Run and Command Modes. 2.5 Forward and Backward Chaining. 2.6 Program Modularization and Blackboard Systems. 2.7 Handling Uncertainties in an Expert System. 2.8 Summary. 2.9 Questions. 3 Fuzzy Logic, Fuzzy Sets, and Fuzzy Numbers: I. 3.1 Classical Logic. 3.2 Elementary Fuzzy Logic and Fuzzy Propositions. 3.3 Fuzzy Sets. 3.4 Fuzzy Relations. 3.5 Truth Value of Fuzzy Propositions. 3.6 Fuzzification and Defuzzification. 3.7 Questions. 4 Fuzzy Logic, Fuzzy Sets, and Fuzzy Numbers: II. 4.1 Introduction. 4.2 Algebra of Fuzzy Sets. 4.3 Approximate Reasoning. 4.4 Hedges. 4.5 Fuzzy Arithmetic. 4.6 Comparisons between Fuzzy Numbers. 4.7 Fuzzy Propositions. 4.8 Questions. 5 Combining Uncertainties. 5.1 Generalizing AND and OR Operators. 5.2 Combining Single Truth Values. 5.3 Combining Fuzzy Numbers and Membership Functions. 5.4 Bayesian Methods. 5.5 The Dempster-Shafer Method. 5.6 Summary. 5.7 Questions. 6 Inference in an Expert System I. 6.1 Overview. 6.2 Types of Fuzzy Inference. 6.3 Nature of Inference in a Fuzzy Expert System. 6.4 Modification and Assignment of Truth Values. 6.5 Approximate Reasoning. 6.6 Tests of Procedures to Obtain the Truth Value of a Consequent from the Truth Value of Its Antecedent. 6.7 Summary. 6.8 Questions. 7 Inference in a Fuzzy Expert System II: Modification of Data and Truth Values. 7.1 Modification of Existing Data by Rule Consequent Instructions. 7.2 Modification of Numeric Discrete Fuzzy Sets: Linguistic Variables and Linguistic Terms. 7.3 Selection of Reasoning Type and Grade-of-Membership Initialization. 7.4 Fuzzification and Defuzzification. 7.5 Non-numeric Discrete Fuzzy Sets. 7.6 Discrete Fuzzy Sets: Fuzziness, Ambiguity, and Contradiction. 7.7 Invalidation of Data: Non-monotonic Reasoning. 7.8 Modification of Values of Data. 7.9 Modeling the Entire Rule Space. 7.10 Reducing the Number of Classification Rules Required in the Conventional Intersection Rule Configuration. 7.11 Summary. 7.12 Questions. 8 Resolving Contradictions: Possibility and Necessity. 8.1 Definition of Possibility and Necessity. 8.2 Possibility and Necessity Suitable for MultiStep Rule-Based Fuzzy Reasoning. 8.3 Modification of Truth Values During a Fuzzy Reasoning Process. 8.4 Formulation of Rules for Possibility and Necessity. 8.5 Resolving Contradictions Using Possibility in a Necessity-Based System. 8.6 Summary. 8.7 Questions. 9 Expert System Shells and the Integrated Development Environment (IDE). 9.1 Overview. 9.2 Help Files. 9.3 Program Editing. 9.4 Running the Program. 9.5 Features of General-Purpose Fuzzy Expert Systems. 9.6 Program Debugging. 9.7 Summary. 9.8 Questions. 10 Simple Example Programs. 10.1 Simple FLOPS Programs. 10.2 Numbers.fps. 10.3 Sum.fps. 10.4 Sum.par. 10.5 Comparison of Serial and Parallel FLOPS. 10.6 Membership Functions, Fuzzification and Defuzzification. 10.7 Summary. 10.8 Questions. 11 Running and Debugging Fuzzy Expert Systems I: Parallel Programs. 11.1 Overview. 11.2 Debugging Tools. 11.3 Debugging Short Simple Programs. 11.4 Isolating the Bug: System Modularization. 11.5 The Debug Run. 11.6 Interrupting the Program for Debug Checks. 11.7 Locating Program Defects with Debug Commands. 11.8 Summary. 11.9 Questions. 12 Running and Debugging Expert Systems II: Sequential Rule-Firing. 12.1 Data Acquisition: From a User Versus Automatically Acquired. 12.2 Ways of Solving a Tree-Search Problem. 12.3 Expert Knowledge in Rules auto1.fps. 12.4 Expert Knowledge in a Database: auto2.fps. 12.5 Other Applications of Sequential Rule Firing. 12.5.1 Missionaries and Cannibals. 12.6 Rules that Make Themselves Refireable: Runaway Programs and Recursion. 12.7 Summary. 12.8 Questions. 13 Solving "What?" Problems when the Answer is Expressed in Words. 13.1 General Methods. 13.2 Iris.par: What Species Is It? 13.3 Echocardiogram Pattern Recognition. 13.4 Schizo.par. 13.5 Discussion. 13.6 Questions. 14 Programs that Can Learn from Experience. 14.1 General Methods. 14.2 Pavlov1.par: Learning by Adding Rules. 14.3 Pavlov2.par: Learning by Adding Facts to Long-Term Memory. 14.4 Defining New Data Elements and New: RULEGEN.FPS. 14.5 Most General Way of Creating New Rules and Data Descriptors. 14.6 Discussion. 14.7 Questions. 15 Running On-Line in Real-Time. 15.1 Overview of On-Line Real-Time Work. 15.2 Input/Output On-Line in Real-Time. 15.3 On-Line Real-Time Processing. 15.4 Types of Rules Useful in Real-Time On-Line Work. 15.5 Memory Management. 15.6 Development of On-Line Real-Time Programs. 15.7 Speeding Up a Program. 15.8 Debugging Real-Time Online Programs. 15.9 Discussion. 15.10 Questions. Appendix. Answers. References. Index.

Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics

Abstract: 1 Introduction.- 2 Mathematical Basics for the Formal Description of Uncertainty.- 3 Description of Uncertain Structural Parameters as Fuzzy Variables.- 4 Description of Uncertain Structural Parameters as Fuzzy Random Variables.- 5 Fuzzy and Fuzzy Stochastic Structural Analysis.- 6 Fuzzy Probabilistic Safety Assessment.- 7 Structural Design Based on Clustering.- References.

Flexible neuro-fuzzy systems

Abstract: In this paper, we derive new neuro-fuzzy structures called flexible neuro-fuzzy inference systems or FLEXNFIS. Based on the input-output data, we learn not only the parameters of the membership functions but also the type of the systems (Mamdani or logical). Moreover, we introduce: 1) softness to fuzzy implication operators, to aggregation of rules and to connectives of antecedents; 2) certainty weights to aggregation of rules and to connectives of antecedents; and 3) parameterized families of T-norms and S-norms to fuzzy implication operators, to aggregation of rules and to connectives of antecedents. Our approach introduces more flexibility to the structure and design of neuro-fuzzy systems. Through computer simulations, we show that Mamdani-type systems are more suitable to approximation problems, whereas logical-type systems may be preferred for classification problems.

Non-dual fuzzy connections

Abstract: The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results; – interesting new concepts besides antitone and isotone ones (like, for instance, conjugated pair), that were classically reducible to the first, gain independency in fuzzy setting.

A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Abstract: Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked.

Online tuning of fuzzy inference systems using dynamic fuzzy Q-learning

Abstract: This paper presents a dynamic fuzzy Q-learning (DFQL) method that is capable of tuning fuzzy inference systems (FIS) online. A novel online self-organizing learning algorithm is developed so that structure and parameters identification are accomplished automatically and simultaneously based only on Q-learning. Self-organizing fuzzy inference is introduced to calculate actions and Q-functions so as to enable us to deal with continuous-valued states and actions. Fuzzy rules provide a natural mean of incorporating the bias components for rapid reinforcement learning. Experimental results and comparative studies with the fuzzy Q-learning (FQL) and continuous-action Q-learning in the wall-following task of mobile robots demonstrate that the proposed DFQL method is superior.

Fuzzy Neural Network Theory and Application

Abstract: Fuzzy Neural Networks for Storing and Classifying Feedback Fuzzy Associative Memory Regular Fuzzy Neural Networks Polygonal Fuzzy Neural Networks Approximation Analysis of Fuzzy Systems Stochastic Fuzzy Systems and Approximation Application of Fuzzy Neural Networks to Image Restoration

Evolutionary design of a fuzzy classifier from data

Abstract: Genetic algorithms show powerful capabilities for automatically designing fuzzy systems from data, but many proposed methods must be subjected to some minimal structure assumptions, such as rule base size. In this paper, we also address the design of fuzzy systems from data. A new evolutionary approach is proposed for deriving a compact fuzzy classification system directly from data without any a priori knowledge or assumptions on the distribution of the data. At the beginning of the algorithm, the fuzzy classifier is empty with no rules in the rule base and no membership functions assigned to fuzzy variables. Then, rules and membership functions are automatically created and optimized in an evolutionary process. To accomplish this, parameters of the variable input spread inference training (VISIT) algorithm are used to code fuzzy systems on the training data set. Therefore, we can derive each individual fuzzy system via the VISIT algorithm, and then search the best one via genetic operations. To evaluate the fuzzy classifier, a fuzzy expert system acts as the fitness function. This fuzzy expert system can effectively evaluate the accuracy and compactness at the same time. In the application section, we consider four benchmark classification problems: the iris data, wine data, Wisconsin breast cancer data, and Pima Indian diabetes data. Comparisons of our method with others in the literature show the effectiveness of the proposed method.

Opening the black box of neural networks for remote sensing image classification

Abstract: Neural networks, which make no assumption about data distribution, have achieved improved image classification results compared to traditional methods. Unfortunately, a neural network is generally perceived as being a ‘black box’. It is extremely difficult to document how specific classification decisions are reached. Fuzzy systems, on the other hand, have the capability to represent classification decisions explicitly in the form of fuzzy ‘if-then’ rules. However, the construction of a knowledge base, especially the fine-tuning of the fuzzy set parameters of the fuzzy rules in a fuzzy expert system, is a tedious and subjective process. This research has developed a new, improved neuro-fuzzy image classification system based on the synergism between neural networks and fuzzy expert systems. It incorporates the best of both technologies and compensates for the shortcomings of each. The learning algorithms of neural networks developed here are used to automate the derivation of fuzzy set parameters for the ...

Automatic generation control of an interconnected hydro-thermal system using conventional integral and fuzzy logic controller

Abstract: This paper deals with automatic generation control of interconnected hydrothermal system in the continuous-discrete mode using conventional integral and fuzzy logic controllers. Effects of variation of sampling time period on dynamic responses have been investigated, both with conventional integral controller and fuzzy logic controllers, considering small step perturbations. Effects of different number of triangular membership functions and inputs for fuzzy logic controller on dynamic response have been explored. Further, dynamic responses under small step perturbation have been compared, considering integral and fuzzy logic controllers.

Matrix Games with Fuzzy Goals and Fuzzy Linear Programming Duality

Abstract: A two person zero-sum matrix game with fuzzy goals is shown to be equivalent to a primal-dual pair of fuzzy linear programming problems. Further certain difficulties with similar studies reported in the literature are also discussed.

Fuzzy comprehensive evaluation model based on improved analytic hierarchy process

Abstract: The key problem of fuzzy comprehensive evaluation both in theory and practice is how to reasonably quantify the weights of different evaluation indexes in the fuzzy system. In this paper a new approach is proposed to directly construct the judgment matrix in analytic hierarchy process according to the fuzzy relative membership degree matrix of single evaluation index. On this basis, a new method namely analytic hierarchy process-fuzzy comprehensive evaluation (FCE-AHP), which can be used to check and correct the in consistency of judgment matrix by means of accelerated genetic algorithm and to calculate the weight of the elements in the judgment matrix, is established. The application shows that this method is universal, stable and the calculation result is objective.

Comparison of Heuristic Criteria for Fuzzy Rule Selection in Classification Problems

Abstract: This paper compares heuristic criteria used for extracting a pre-specified number of fuzzy classification rules from numerical data. We examine the performance of each heuristic criterion through computational experiments on well-known test problems. Experimental results show that better results are obtained from composite criteria of confidence and support measures than their individual use. It is also shown that genetic algorithm-based rule selection can improve the classification ability of extracted fuzzy rules by searching for good rule combinations. This observation suggests the importance of taking into account the combinatorial effect of fuzzy rules (i.e., the interaction among them).

On generalized measures of fuzzy entropy

Abstract: In the present paper, the existing measures of fuzzy entropy are reviewed. Two new generalized measures of fuzzy entropy are defined and char­ acterized. A new measure of P-normed fuzzy entropy is introduced and charac­ terized. Some generalized measures of fuzzy directed and symmetric divergence are studied and particular cases of the generalized and B-normed fuzzy entropies have also been obtained.

Bi-matrix Games with Fuzzy Goals and Fuzzy

Abstract: A bi-matrix game with fuzzy goal is shown to be equivalent to a (crisp) non-linear programming problem in which the objective as well as all constraint functions are linear except two constraint functions, which are quadratic. This equivalence is further extended to bi-matrix games with fuzzy pay-offs, as well as to bi-matrix games with fuzzy goals and fuzzy payoffs, whose equilibrium strategies are conceptualized by employing a suitable ranking (defuzzification) function.

Principal component analysis of fuzzy data using autoassociative neural networks

Abstract: This paper describes an extension of principal component analysis (PCA) allowing the extraction of a limited number of relevant features from high-dimensional fuzzy data. Our approach exploits the ability of linear autoassociative neural networks to perform information compression in just the same way as PCA, without explicit matrix diagonalization. Fuzzy input values are propagated through the network using fuzzy arithmetics, and the weights are adjusted to minimize a suitable error criterion, the inputs being taken as target outputs. The concept of correlation coefficient is extended to fuzzy numbers, allowing the interpretation of the new features in terms of the original variables. Experiments with artificial and real sensory evaluation data demonstrate the ability of our method to provide concise representations of complex fuzzy data.

New fuzzy control model and dynamic output feedback parallel distributed compensation

Abstract: A new fuzzy modeling based on fuzzy linear fractional transformations model is introduced. This new representation is shown to be a flexible tool for handling complicated nonlinear models. Particularly, the new fuzzy model provides an efficient and tractable way to handle the output feedback parallel distributed compensation problem. We demonstrate that this problem can be given a linear matrix inequality characterization and hence is immediately solvable through available semidefinite programming codes. The capabilities of the new fuzzy modeling is illustrated through numerical examples.

On improvement of stability conditions for continuous Mamdani-like fuzzy systems

Abstract: This paper is concerned with continuous fuzzy systems with singleton consequents, called type II fuzzy systems. It first introduces the canonical form of an unforced type II fuzzy system and its stability theorem presented in the previous study. Then, improving the stability theorem, it gives necessary and sufficient conditions such that a type II fuzzy system is stable with respect to a global quadratic Lyapunov function.

Falcon: neural fuzzy control and decision systems using FKP and PFKP clustering algorithms

Abstract: Neural fuzzy networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. Examples are the Falcon-ART, and the POPFNN family of networks. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. This correspondence proposes two new networks: Falcon-FKP and Falcon-PFKP. They are extensions of the Falcon-ART network, and aimed to overcome the shortcomings faced by the Falcon-ART network itself, i.e., poor classification ability when the classes of input data are very similar to each other, termination of training cycle depends heavily on a preset error parameter, the fuzzy rule base of the Falcon-ART network may not be consistent Nauck, there is no control over the number of fuzzy rules generated, and learning efficiency may deteriorate by using complementarily coded training data. These deficiencies are essentially inherent to the fuzzy ART, clustering technique employed by the Falcon-ART network. Hence, two clustering techniques- Fuzzy Kohonen Partitioning (FKP) and its pseudo variant PFKP, are synthesized with the basic Falcon structure to compute the fuzzy sets and to automatically derive the fuzzy rules from the training data. The resultant neural fuzzy networks are Falcon-FKP and Falcon-PFKP, respectively. These two proposed networks have a lean and efficient training algorithm and consistent fuzzy rule bases. Extensive simulations are conducted using the two networks and their performances are encouraging when benchmarked against other neural and neural fuzzy systems.

Fuzzy approximation by fuzzy convolution type operators

Abstract: Here we introduce and study four sequences of naturally arising fuzzy integral operatorsof convolution type that are integral analogs of known fuzzy wavelet type operators, defined via a scaling function. Their fuzzy convergence with rates to the fuzzy unit operator is established through fuzzy inequalities involving the fuzzy modulus of continuity. Also, their high-order fuzzy approximation is given similarly by involving the fuzzy modulus of continuity of the N^t^h order (N >= 1) H-fuzzy derivative of the engaged fuzzy number valued function. The fuzzy global smoothness preservation property of these operators is demonstrated also.

A Comparative Study of Fuzzy Classification Methods on Breast Cancer Data

Abstract: In this paper, we examine the performance of four fuzzy rule generation methods on Wisconsin breast cancer data. The first method generates fuzzy if-then rules using the mean and the standard deviation of attribute values with 92.2% correct classification rate. The second approach generates fuzzy if-then rules using the histogram of attributes values with 86.7% correct classification rate. The third procedure generates fuzzy if-then rules with certainty of each attribute into homogeneous fuzzy sets with 99.73% correct classification rate. In the fourth approach, only overlapping areas are partitioned with 62.57% correct classification rate. The first two approaches generate a single fuzzy if-then rule for each class by specifying the membership function of each antecedent fuzzy set using the information about attribute values of training patterns. The other two approaches are based on fuzzy grids with homogeneous fuzzy partitions of each attribute. The performance of each approach is evaluated on breast cancer data sets. Simulation results show that the simple grid approach has a high classification rate of 99.73 %.

Hardware architecture and FPGA implementation of a type-2 fuzzy system

Abstract: This paper presents an architectural proposal for a hardware-based interval type-2 fuzzy inference system. First, it presents a computational model which considers parallel inference processing and type reduction based on computing inner and outer bound sets. Taking into account this model, we conceived a hardware architecture with several pipeline stages for full parallel execution of type-2 fuzzy inferences. The architectural proposal is used for specifying a type-2 fuzzy processor with reconfigurable rule base, which is implemented over FPGA technology. Implementation results show that this processor performs more than 30 millions of type-2 fuzzy inferences per second.

On priority method of triangular fuzzy number complementary judgement matrix

Abstract: This paper studies the multi-attribute decision making problem, in which the decision information takes the form of triangular fuzzy number complementary judgement matrix. Some concepts such as triangular fuzzy number consistent complementary judgement matrix, etc., are given and a linear objective programming model is established. The weight vector of triangular fuzzy complementary judgement matrix is obtained by solving the model. By using a existing priority formula of triangular fuzzy numbers, the decision alternatives are ranked. Finally, a numerical example is given.