Rutkowska, Danuta - ed. ; Kacprzyk, Janusz - ed. ; Zadeh, Lotfi A. - ed.
On granular derivatives and the solution of a granular initial value problem
Computing with Words and Perceptions
Group publication title:
Subject and Keywords:
fuzzy differential ; fuzzy granule ; initial value problem ; cylindrical extension
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.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 12, number 3 (2002) ; click here to follow the link