On fuzzy input data and the worst scenario method

Chleboun, Jan. "On fuzzy input data and the worst scenario method." Applications of Mathematics 48.6 (2003): 487-496. <http://eudml.org/doc/33162>.

@article{Chleboun2003,
abstract = {In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set $\mathcal \{U\}_\{\mathrm \{a\}d\}$ of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by $\mathcal \{U\}_\{\mathrm \{a\}d\}$ and maximizes a functional criterion reflecting a particular feature of the state solution, as local stress, displacement, or temperature, for instance. An increase in the criterion value indicates a deterioration in the featured quantity. The method takes all the elements of $\mathcal \{U\}_\{\mathrm \{a\}d\}$ as equally important though this can be unrealistic and can lead to too pessimistic conclusions. Often, however, additional information expressed through a membership function of $\mathcal \{U\}_\{\mathrm \{a\}d\}$ is available, i.e., $\mathcal \{U\}_\{\mathrm \{a\}d\}$ becomes a fuzzy set. In the article, infinite-dimensional $\mathcal \{U\}_\{\mathrm \{a\}d\}$ are considered, two ways of introducing fuzziness into $\mathcal \{U\}_\{\mathrm \{a\}d\}$ are suggested, and the worst scenario method operating on fuzzy admissible sets is proposed to obtain a fuzzy set of outputs.},
author = {Chleboun, Jan},
journal = {Applications of Mathematics},
keywords = {fuzzy sets; uncertainty; worst scenario method; fuzzy sets; uncertainty; worst scenario method},
language = {eng},
number = {6},
pages = {487-496},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On fuzzy input data and the worst scenario method},
url = {http://eudml.org/doc/33162},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Chleboun, Jan
TI - On fuzzy input data and the worst scenario method
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 6
SP - 487
EP - 496
AB - In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set $\mathcal {U}_{\mathrm {a}d}$ of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by $\mathcal {U}_{\mathrm {a}d}$ and maximizes a functional criterion reflecting a particular feature of the state solution, as local stress, displacement, or temperature, for instance. An increase in the criterion value indicates a deterioration in the featured quantity. The method takes all the elements of $\mathcal {U}_{\mathrm {a}d}$ as equally important though this can be unrealistic and can lead to too pessimistic conclusions. Often, however, additional information expressed through a membership function of $\mathcal {U}_{\mathrm {a}d}$ is available, i.e., $\mathcal {U}_{\mathrm {a}d}$ becomes a fuzzy set. In the article, infinite-dimensional $\mathcal {U}_{\mathrm {a}d}$ are considered, two ways of introducing fuzziness into $\mathcal {U}_{\mathrm {a}d}$ are suggested, and the worst scenario method operating on fuzzy admissible sets is proposed to obtain a fuzzy set of outputs.
LA - eng
KW - fuzzy sets; uncertainty; worst scenario method; fuzzy sets; uncertainty; worst scenario method
UR - http://eudml.org/doc/33162
ER -