Towards a linguistic description of dependencies in data

Ildar Batyrshin; Michael Wagenknecht

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 3, page 391-401
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Batyrshin, Ildar, and Wagenknecht, Michael. "Towards a linguistic description of dependencies in data." International Journal of Applied Mathematics and Computer Science 12.3 (2002): 391-401. <http://eudml.org/doc/207596>.

@article{Batyrshin2002,
abstract = {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.},
author = {Batyrshin, Ildar, Wagenknecht, Michael},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {genetic algorithm; linguistic term; fuzzy rule; fuzzy approximation},
language = {eng},
number = {3},
pages = {391-401},
title = {Towards a linguistic description of dependencies in data},
url = {http://eudml.org/doc/207596},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Batyrshin, Ildar
AU - Wagenknecht, Michael
TI - Towards a linguistic description of dependencies in data
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 3
SP - 391
EP - 401
AB - 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.
LA - eng
KW - genetic algorithm; linguistic term; fuzzy rule; fuzzy approximation
UR - http://eudml.org/doc/207596
ER -

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