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2002 | 12 | 3 | 403-410
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
12
Numer
3
Strony
403-410
Opis fizyczny
Daty
wydano
2002
otrzymano
2002-03-01
poprawiono
2002-06-01
Twórcy
  • Institute of Problems of Informatics, Academy of Sciences of Tatarstan and Kazan State Technological University, K. Marx Str., 68, Kazan, 420015, Russia
Bibliografia
  • Batyrshin I. and Fatkullina R. (1995): Context-dependent fuzzy scales and context-free rules for dependent variables. - Proc. 6-th Int. Fuzzy Systems Association World Congress, IFSA'95, Sao Paulo, Brasil, Vol. 1, pp. 89-91.
  • Batyrshin I. and Panova A. (2001): On granular description of dependencies. -Proc. 9-th Zittau Fuzzy Colloquium, Zittau, Germany, pp. 1-8.
  • Batyrshin I., Zakuanov R. and Bikushev G. (1994): Expert system based on algebra of uncertainties with memory in process optimization. - Proc. 1-st Int. Workshop Fuzzy Logic and Intelligent Technologies in Nuclear Science, Mol, Belgium, World Scientific, pp. 156-159.
  • De Kleer J. and Brawn J. (1984): A qualitative physics based on confluences. -Artif. Intell., Vol. 24, pp. 7-83.
  • Dubois D. and Prade H. (1982): Towards fuzzy differential calculus: Part 3: Differentiation. - Fuzzy Sets Syst., Vol. 8, pp. 225-233.
  • Forbus K.D. (1984): Qualitative process theory. - Artif. Intell., Vol. 24, pp. 85-168.
  • Jang J.S.R., Sun C.T. and Mizutani E. (1997): Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence. - New York: Prentice Hall.
  • Kuipers B. (1984): Commonsense reasoning about causality: deriving behavior from structure. - Artif. Intell., Vol. 24, pp. 169-203.
  • Ma M., Friedman M. and Kandel A. (1999): Numerical solutions of fuzzy differential equations. - Fuzzy Sets Syst., Vol. 105, pp. 133-138.
  • Nieto J.J. (1999): The Cauchy problem for continuous fuzzy differential equations. - Fuzzy Sets and Syst., Vol. 102, pp. 259-262.
  • Park J.K. and Han H.K. (2000): Fuzzy differential equations. - Fuzzy Sets Syst., Vol. 110, pp. 69-77.
  • Song S. and Wu C. (2000): Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations. - Fuzzy Sets Syst., Vol. 110, pp. 55-67.
  • Vorobiev D. and Seikkala S. (2002): Towards the theory of fuzzy differential equations. - Fuzzy Sets Syst., Vol. 125, pp. 231-237.
  • Zadeh L.A. (1966): The shadows of fuzzy sets. - Problems of Information Transmission, Vol. 2, pp. 37-44 (in Russian).
  • Zadeh L.A. (1975): The concept of a linguistic variable and its application to approximate reasoning, Part I. - Inf. Sci., Vol. 8, pp. 199-249; Part II. - Inf. Sci., Vol. 8, pp. 301-357; Part III - Inf. Sci., Vol. 9, pp. 43-80.
  • Zadeh L.A. (1997): Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. - Fuzzy Sets Syst., Vol. 90, pp. 111-127.
  • Zadeh L.A. (1999): From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions. - IEEE Trans. Circ. Syst. - 1: Fund. Th. Applic., Vol. 45, No. 1, pp. 105-119.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv12i3p403bwm
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