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Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.


Papers
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Journal ArticleDOI
TL;DR: A new method of finding the fuzzy weights in fuzzy hierarchical analysis is presented, which is the direct fuzzification of the λ max method, used by Saaty in the analytical hierarchical process.

476 citations

Proceedings ArticleDOI
08 Mar 1992
TL;DR: The authors develop a training algorithm, similar to the backpropagation algorithm for neural networks, to train fuzzy systems to match desired input-output pairs and demonstrate how the fuzzy system learns to match an unknown nonlinear mapping as training progresses and that performance is improved by incorporating linguistic rules.
Abstract: The authors develop a training algorithm, similar to the backpropagation algorithm for neural networks, to train fuzzy systems to match desired input-output pairs. The key ideas in developing this training algorithm are to view a fuzzy system as a three-layer feedforward network, and to use the chain rule to determine gradients of the output errors of the fuzzy system with respect to its design parameters. It is shown that this training algorithm performs an error backpropagation procedure: hence, the fuzzy system equipped with the backpropagation training algorithm is called the backpropagation fuzzy system (BP FS). An online initial parameter choosing method is proposed for the BP FS, and it is shown that it is straightforward to incorporate linguistic if-then rules into the BP FS. Two examples are presented which demonstrate (1) how the fuzzy system learns to match an unknown nonlinear mapping as training progresses and (2) that performance is improved by incorporating linguistic rules. >

475 citations

Journal ArticleDOI
TL;DR: A survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory.

474 citations

Journal ArticleDOI
TL;DR: The basic theory of the triangular fuzzy number is proved and the formulation of comparing the triangular fuzziness number's size is improved, and a practical example on petroleum prospecting is introduced.

472 citations

Journal ArticleDOI
Yaochu Jin1
TL;DR: This paper proposes an effective approach to data-based fuzzy modeling of high-dimensional systems by generating an initial fuzzy rule system based on the conclusion that optimal fuzzy rules cover extrema using a genetic algorithm and the gradient method.
Abstract: Fuzzy modeling of high-dimensional systems is a challenging topic. This paper proposes an effective approach to data-based fuzzy modeling of high-dimensional systems. An initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema. Redundant rules are removed based on a fuzzy similarity measure. Then, the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method. During optimization, rules that have a very low firing strength are deleted. Finally, interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization. The resulting fuzzy system generated by this method has the following distinct features: (1) the fuzzy system is quite simplified; (2) the fuzzy system is interpretable; and (3) the dependencies between the inputs and the output are clearly shown. This method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data.

470 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023202
2022446
2021696
2020649
2019653
2018733