# On granular derivatives and the solution of a granular initial value problem

• Volume: 12, Issue: 3, page 403-410
• ISSN: 1641-876X

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## Abstract

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Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s piecewise linear solution of an initial value problem. The solution method is based on a granulation of the directions of the function change, on an extension of the initial value in directions and on a propagation of fuzzy constraints given in antecedent parts of rules on possible function values. The proposed method is illustrated with an example.

## How to cite

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Batyrshin, Ildar. "On granular derivatives and the solution of a granular initial value problem." International Journal of Applied Mathematics and Computer Science 12.3 (2002): 403-410. <http://eudml.org/doc/207597>.

@article{Batyrshin2002,
abstract = {Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s piecewise linear solution of an initial value problem. The solution method is based on a granulation of the directions of the function change, on an extension of the initial value in directions and on a propagation of fuzzy constraints given in antecedent parts of rules on possible function values. The proposed method is illustrated with an example.},
author = {Batyrshin, Ildar},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {initial value problem; fuzzy differential; fuzzy granule; cylindrical extension},
language = {eng},
number = {3},
pages = {403-410},
title = {On granular derivatives and the solution of a granular initial value problem},
url = {http://eudml.org/doc/207597},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Batyrshin, Ildar
TI - On granular derivatives and the solution of a granular initial value problem
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 3
SP - 403
EP - 410
AB - Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s piecewise linear solution of an initial value problem. The solution method is based on a granulation of the directions of the function change, on an extension of the initial value in directions and on a propagation of fuzzy constraints given in antecedent parts of rules on possible function values. The proposed method is illustrated with an example.
LA - eng
KW - initial value problem; fuzzy differential; fuzzy granule; cylindrical extension
UR - http://eudml.org/doc/207597
ER -

## References

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