Fuzzy finite element

The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case of a fuzzy set.[1] The advantage of using fuzzy numbers instead of real numbers lies in the incorporation of uncertainty (on material properties, parameters, geometry, initial conditions, etc.) in the finite element analysis.

One way to establish a fuzzy finite element (FE) analysis is to use existing FE software (in-house or commercial) as an inner-level module to compute a deterministic result, and to add an outer-level loop to handle the fuzziness (uncertainty). This outer-level loop comes down to solving an optimization problem. If the inner-level deterministic module produces monotonic behavior with respect to the input variables, then the outer-level optimization problem is greatly simplified, since in this case the extrema will be located at the vertices of the domain.

## See also

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* Finite element method
* Fuzzy number
* Fuzzy set
* Uncertainty

## References

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1. ^ Michael Hanss, 2005. Applied Fuzzy Arithmetic, An Introduction with Engineering Applications. Springer, ISBN 3-540-24201-5

* v
* t
* e

Non-classical logic

Intuitionistic|

* Intuitionistic logic
* Constructive analysis
* Heyting arithmetic
* Intuitionistic type theory
* Constructive set theory

Fuzzy|

* Degree of truth
* Fuzzy rule
* Fuzzy set
* Fuzzy finite element
* Fuzzy set operations

Substructural|

* Structural rule
* Relevance logic
* Linear logic

Paraconsistent|

* Dialetheism

Description|

* Ontology (information science)
* Ontology language

Many-valued|

* Three-valued
* Four-valued
* Łukasiewicz

Digital logic|

* Three-state logic
* Tri-state buffer
* Four-valued
* Verilog
* IEEE 1164
* VHDL

Others|

* Dynamic semantics
* Inquisitive logic
* Intermediate logic
* Non-monotonic logic

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