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

100%

Batyrshin I.

International Journal of Applied Mathematics and Computer Science

2002

tom 12

nr 3

403-410

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.

Towards a linguistic description of dependencies in data

63%

Batyrshin I., Wagenknecht M.

International Journal of Applied Mathematics and Computer Science

2002

tom 12

nr 3

391-401

The problem of a linguistic description of dependencies in data by a set of rules R_k: “If X is T_k then Y is S_k” is considered, where T_k’s are linguistic terms like SMALL, BETWEEN 5 AND 7 describing some fuzzy intervals A_k. S_k’s are linguistic terms like DECREASING and QUICKLY INCREASING describing the slopes p_k of linear functions y_k = p_{k}x + q_k approximating data on A_k. The decision of this problem is obtained as a result of a fuzzy partition of the domain X on fuzzy intervals A_k, approximation of given data {x_i, y_i}, i = 1, . . . , n by linear functions y_k = p_{k}x + q_k on these intervals and by re-translation of the obtained results into linguistic form. The properties of the genetic algorithm used for construction of the optimal partition and several methods of data re-translation are described. The methods are illustrated by examples, and potential applications of the proposed methods are discussed.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

2 Batyrshin I.

1 Wagenknecht M.

2 2002

Wyniki wyszukiwania

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

Towards a linguistic description of dependencies in data