Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
Papers published on a yearly basis
Papers
More filters
Book•
11 Jan 2002
TL;DR: Fuzzy Sets, Fuzzy Numbers, and Genetic Algorithms - A Beginner's Guide to FuzzY Optimization.
Abstract: 1 Introduction.- 2 Logic.- 3 Fuzzy Sets.- 4 Fuzzy Numbers.- 5 Fuzzy Equations.- 6 Fuzzy Inequalities.- 7 Fuzzy Relations.- 8 Fuzzy Functions.- 9 Fuzzy Plane Geometry.- 10 Fuzzy Trigonometry.- 11 Systems of Fuzzy Linear Equations.- 12 Possibility Theory.- 13 Neural Nets.- 14 Approximate Reasoning.- 15 Genetic Algorithms.- 16 Fuzzy Optimization.- List of Figures.- List of Tables.
269 citations
01 Jan 1971
TL;DR: A method of classifying patterns using fuzzy relations is described, where a similitude between any two patterns is calculated by using the composition of a fuzzy relation to induce an equivalence relation.
Abstract: A method of classifying patterns using fuzzy relations is described. To start with, we give a suitable value of the measure of subjective similarity to each pair of patterns that is taken from the population of patterns to be classified. Then a similitude between any two patterns is calculated by using the composition of a fuzzy relation. The similitude induces an equivalence relation. Consequently, we can classify the present population of the patterns into some classes by the equivalence relation. An experiment of the classification of portraits has been performed to test the method proposed here.
269 citations
Book•
01 Jan 2004
TL;DR: This approach introduces more flexibility to the structure and design of neuro-fuzzy systems, and shows that Mamdani- type systems are more suitable to approximation problems, whereas logical-type systems may be preferred for classification problems.
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.
268 citations
Book•
11 May 2000
TL;DR: Approximate Reasoning: Interpretation of Fuzzy Conditional Statement Using Different Interpretations of If-Then Rules, and an Approach to Axiomatic Definition of FBuzzy Implication.
Abstract: Classical Sets and Fuzzy Sets. Basic Definitions and Terminology: Classical Sets. Fuzzy Sets. Operations on Fuzzy Sets. Classification of t-Norms and t-Conorms. De Morgan Triple and Other Properties of t- and s-Norms. Parameterized t-, s-Norms and Negations. Fuzzy Relations. Cylindrical Extension and Projection of Fuzzy Sets. Extension Principle. Linguistic Variable. Summary.- Approximate Reasoning: Interpretation of Fuzzy Conditional Statement. An Approach to Axiomatic Definition of Fuzzy Implication. Compositional Rule of Inference. Fuzzy Reasoning. Canonical Fuzzy If-Then Rule. Aggregation Operation. Approximate Reasoning Using a Fuzzy Rule Base. Approximate Reasoning with Singletons. Fuzzifiers and Defuzzifiers. Equivalence of Approximate Reasoning Results Using Different Interpretations of If-Then Rules. Numerical Results. Summary.- Artificial Neural Networks: Introduction. Artificial Neural Networks Topologies. Learning in Artificial Neural Networks. Back-Propagation Learning Rule. Modifications of the Classic Back-Propagation Method. Optimization Methods in Neural Networks Learning. Networks with Output Linearly Depending on Parameters. Global Optimization Methods. Summary.- Unsupervised Learning. Clustering Methods: Introduction. Self-Organizing Feature Map. Vector Quantization and Learning Vector Quantization. An Overview of Clustering Methods. Fuzzy Clustering Methods. A Possibilistic Approach to Clustering. A New Generalized Weighted Conditional Fuzzy c-Means. Fuzzy Learning Vector Quantization. Cluster Validity. Summary.- Fuzzy Systems: Introduction. The Mamdani Fuzzy Systems. The Tagaki-Sugeno-Kang Fuzzy Systems. Fuzzy Systems with Parametrized Consequents. Summary.- Neuro-Fuzzy Systems: Introduction. Artificial Neural Network Based Fuzzy Inference Systems. Classifier Based On Neuro-Fuzzy System. ANNBFIS Optimization Using Deterministic Annealing. Further Investigations of Neuro-Fuzzy Systems. Summary.- Applications of Artificial Neural Network Based Fuzzy Inference System: Introduction. Application to Chaotic Time Series Prediction. Application to ECG Signal Compression. Application to Ripley's Synthetic Two-Class Data Classification. Application to the Recognition of Diabetes in Pima Indians. Application to the Iris Problem. Application to Monk's Problems. Application to System Identification. Application to Control. Application to Channel Equalization. Summary.
268 citations
TL;DR: A scheme based on the classical Euler method is discussed in detail, and this is followed by a complete error analysis, illustrated by solving several linear and nonlinear fuzzy Cauchy problems.
268 citations