A type 2 adaptive fuzzy inferencing system
Published 27 November 2002
Robert John, C. Czarnecki
Citations39
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TL;DR
This work aims to extend the adaptive network based fuzzy inferencing system (ANFIS) for type 2 systems with inputs that are linguistic variables and the membership functions for these fuzzy grades are learnt from the relationship between these inputs and the given output.
Abstract
Type 2 fuzzy sets allow for linguistic grades of membership and, therefore, present a better representation of the 'fuzziness', when applied to a particular problem, than type 1 fuzzy sets. However, the associated cost is that the fuzzy membership grades and rules have somehow to be determined and no recognised approach yet exists. For type 1 systems a number of approaches have been adopted. One in particular is the adaptive network based fuzzy inferencing system (ANFIS) which has successfully been applied to a variety of applications. ANFIS takes domain data and learns the membership functions and rules for a type 1 fuzzy inferencing system. Our work aims to extend this approach for type 2 systems. Our Type 2 adaptive fuzzy inferencing system has inputs that are linguistic variables and the membership functions for these fuzzy grades are learnt from the relationship between these inputs and the given output. The paper describes the algorithm developed highlighting the theoretical and computational issues involved.
Keywords
Computer ScienceDecision Sciences
IEEE Transactions on Systems Man and CyberneticsANFIS: adaptive-network-based fuzzy inference system
16,152 Citations1993Jyh‐Shing Roger Jang
The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference System implemented in the framework of adaptive networks.
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning-III
12,148 Citations1975L. A. Zadeh
Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—I
12,036 Citations1975Lotfi A. Zadeh
It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc.
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—II
2,509 Citations1975Lotfi A. Zadeh
The nonrestricted nonfuzzy variable u constitutes the base variable for X and R(X;u) is a fuzzy subset of U which represents a fuzzy restriction on the values of u imposed by X.
Proceedings of the IEEEFuzzy logic systems for engineering: a tutorial
2,073 Citations1995Jerry M. Mendel
After synthesizing a FLS, it is demonstrated that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks.
Information and ControlSome properties of fuzzy sets of type 2
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International Journal of Approximate ReasoningNN-driven fuzzy reasoning
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Journal of CyberneticsFUZZY SUBSETS OF TYPE II IN DECISIONS
181 Citations1980Ronald R. Yager
The construction of an ideal decision function from its approximation in terms of other decision functions is interested, and fuzzy subsets of type II, those with linguistic grades of membership, are investigated.
IEEE SpectrumAdaptive fuzzy systems
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Conventional fuzzy control systems using PID (proportional-integral-derivative) control and their limitations are discussed and ways to incorporate adaptivity are examined.
John Wiley & Sons, Inc. eBooksIntelligent Systems for Finance and Business
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Fuzzy Sets and SystemsApplication of fuzzy sets of type 2 to the solution of fuzzy equations systems
106 Citations1988Michael Wagenknecht, K. Hartmann
The situation that the outputs of an object are modelled by fuzzy sets of Type 2, which enables us to define solutions for fuzzy outputs of Type 1, when classical solution concepts may fail.
IEEE Transactions on Fuzzy SystemsA neural fuzzy system with linguistic teaching signals
90 Citations1995Chin‐Teng Lin, Ya-Ching Lu
A neural fuzzy system learning with linguistic teaching signals is proposed that is able to process and learn numerical information as well as linguistic information, and two kinds of learning schemes are developed: fuzzy supervised learning and fuzzy reinforcement learning.
Fuzzy Sets and SystemsGenerating fuzzy membership functions: A monotonic neural network model
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This paper suggests that neural networks which use the back propagation learning algorithm under monotonic function constraints can be used in generating fuzzy membership functions.
Type 2 fuzzy sets for knowledge representation and inferencing
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The various approaches to knowledge representation and inferencing are discussed, with worked examples, and some of the applications of type 2 sets are reported.
Fuzzy Sets and SystemsHigher level fuzzy numbers arising from fuzzy regression models
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MLE can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness, when all fuzzy numbers are triangular and the Ei are uniformly distributed.
Journal of the Operational Research SocietyThe use of fuzzy sets for resource allocation in an advance request vehicle brokerage system—a case study
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