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.

References

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

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

[1]

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 (computer 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

See also

References