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Mathematical Modelling
Article
License: Elsevier Non-Commercial
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Mathematical Modelling
Article . 1987
License: Elsevier Non-Commercial
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Mathematical Modelling
Article . 1987 . Peer-reviewed
License: Elsevier Non-Commercial
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Fuzzy models and relational equations

Authors: Witold Pedrycz;

Fuzzy models and relational equations

Abstract

The paper addresses a problem of system modelling in a fuzzy environment. Firstly a general methodological framework is proposed and in the sequel it is specialized in form of an iterative procedure comprising three basic steps, namely structure determination, parameter estimation and model validation. A state-of-the-art of fuzzy modelling is discussed in detail: some advantages and existing drawbacks are carefully analyzed. Also a variety of forms of fuzzy models are handled in a uniform fashion by means of fuzzy relational equations. In the sequel attention is focused to the determination of a fuzzy relation of the model on the basis of input-output pairs of data available. The paper summarizes existing approaches useful for solving a set of fuzzy relational equations being of analytical as well as numerical character. Finally an original concept of fuzzy confidence interval expressing relevance of the fuzzy model constructed on the basis of collected data is introduced. In one extreme case (perfect fit of the data to the model) this confidence interval reduces to a single value of membership function, while in the second extreme situation the confidence interval expands into a whole \([0,1]\) interval (which indicates complete lack of model relevance).

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Keywords

Fuzzy analysis in statistics, fuzzy confidence interval, system modelling in a fuzzy environment, Fuzzy sets and logic (in connection with information, communication, or circuits theory), fuzzy relational equations, fuzzy modelling, Engineering(all), General theory of mathematical modeling

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
14
Average
Top 10%
Average
hybrid