Fuzzy rule

About: Fuzzy rule is a research topic. Over the lifetime, 7712 publications have been published within this topic receiving 147997 citations.

Fuzzy identification of systems and its applications to modeling and control

Abstract: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented. The premise of an implication is the description of fuzzy subspace of inputs and its consequence is a linear input-output relation. The method of identification of a system using its input-output data is then shown. Two applications of the method to industrial processes are also discussed: a water cleaning process and a converter in a steel-making process.

Generating fuzzy rules by learning from examples

Abstract: A general method is developed to generate fuzzy rules from numerical data. The method consists of five steps: divide the input and output spaces of the given numerical data into fuzzy regions; generate fuzzy rules from the given data; assign a degree of each of the generated rules for the purpose of resolving conflicts among the generated rules; create a combined fuzzy rule base based on both the generated rules and linguistic rules of human experts; and determine a mapping from input space to output space based on the combined fuzzy rule base using a defuzzifying procedure. The mapping is proved to be capable of approximating any real continuous function on a compact set to arbitrary accuracy. Applications to truck backer-upper control and time series prediction problems are presented. >

Essentials of Fuzzy Modeling and Control

Abstract: From the Publisher: At last, here is a thorough introduction that offers complete coverage of all relevant theory and applications to the rapidly evolving field of fuzzy logic While most other books on the subject tend to be loose collections of papers reporting on the state of this or that fuzzy area, Essentials of Fuzzy Modeling and Control follows a logical, pedagogically consistent format designed to fully acquaint readers with the entire range of fuzzy concepts, tools, and modeling techniques While it is an excellent general introduction for students, the authors' ultimate goal is to give researchers an opportunity to acquire everything they need to build the kinds of fuzzy rule-based models used in the development of the controllers now being constructed for the next generation of intelligent systems

A first course in fuzzy logic

Abstract: THE CONCEPT OF FUZZINESS Examples Mathematical modeling Some operations on fuzzy sets Fuzziness as uncertainty Exercises SOME ALGEBRA OF FUZZY SETS Boolean algebras and lattices Equivalence relations and partitions Composing mappings Isomorphisms and homomorphisms Alpha-cuts Images of alpha-level sets Exercises FUZZY QUANTITIES Fuzzy quantities Fuzzy numbers Fuzzy intervals Exercises LOGICAL ASPECTS OF FUZZY SETS Classical two-valued logic A three-valued logic Fuzzy logic Fuzzy and Lukasiewicz logics Interval-valued fuzzy logic Canonical forms Notes on probabilistic logic Exercises BASIC CONNECTIVES t-norms Generators of t-norms Isomorphisms of t-norms Negations Nilpotent t-norms and negations t-conorms DeMorgan systems Groups and t-norms Interval-valued fuzzy sets Type- fuzzy sets Exercises ADDITIONAL TOPICS ON CONNECTIVES Fuzzy implications Averaging operators Powers of t-norms Sensitivity of connectives Copulas and t-norms Exercises FUZZY RELATIONS Definitions and examples Binary fuzzy relations Operations on fuzzy relations Fuzzy partitions Fuzzy relations as Chu spaces Approximate reasoning Approximate reasoning in expert systems A simple form of generalized modus ponens The compositional rule of inference Exercises UNIVERSAL APPROXIMATION Fuzzy rule bases Design methodologies Some mathematical background Approximation capability Exercises POSSIBILITY THEORY Probability and uncertainty Random sets Possibility measures Exercises PARTIAL KNOWLEDGE Motivation Belief functions and incidence algebras Monotonicity Beliefs, densities, and allocations Belief functions on infinite sets Note on Mobius transforms of set-functions Reasoning with belief functions Decision making using belief functions Rough sets Conditional events Exercises FUZZY MEASURES Motivation and definitions Fuzzy measures and lower probabilities Fuzzy measures in other areas Conditional fuzzy measures Exercises THE CHOQUET INTEGRAL The Lebesgue integral The Sugeno integral The Choquet integral Exercises FUZZY MODELING AND CONTROL Motivation for fuzzy control The methodology of fuzzy control Optimal fuzzy control An analysis of fuzzy control techniques Exercises Bibliography Answers to Selected Exercises Index on>

Fuzzy systems as universal approximators

Abstract: An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that overlap. The fuzzy system computes a conditional expectation E|Y|X| if we view the fuzzy sets as random sets. Each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state-space geometry. Neural or statistical clustering systems can approximate the unknown fuzzy patches from training data. These adaptive fuzzy systems approximate a function at two levels. At the local level the neural system approximates and tunes the fuzzy rules. At the global level the rules or patches approximate the function. >