Imposing Restrictions on Density Functions Utilised in Computing With Words

• Autorzy: Gemeinder M.
• Języki publikacji: EN

Abstrakty

EN

Applying the generalised extension principle within the area of Computing with Words typically leads to complex maximisation problems. If distributed quantities--such as, e.g., size distributions within human populations--are considered, density functions representing these distributions become involved. Very often the optimising density functions do not resemble those found in nature; for instance, an optimising density function could consist of two single Dirac pulses positioned near the opposite bounds of the interval limiting the possible values of the quantity considered. Therefore, in this article, density functions with certain shapes which enable us to overcome this lack of resemblance are considered. Furthermore, some considerations on solving the resulting maximisation problems are reported.

Słowa kluczowe

EN

computing with words; approximate reasoning; resemblance

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 3
• Strony: 383--390
• Opis fizyczny: Bibliogr. 12 poz., rys., tab., wykr.

Twórcy

autor

Gemeinder M.

• Faculty of Electrical Engineering Chair of Computer Engineering, Fernuniversitat Hagen, 58084 Hagen, Germany,

Bibliografia

• [1] Baker J. E. (1987): Reducing bias and inefficiency in the selection algorithm, In: Genetic Algorithms and their Applications: Proceedings of the 2nd International Conference on Genetic Algorithms (J. J. Grefenstette, Ed.). - Hillsdale, N.J.: Lawrence Erlbaum Associates, Inc., Publishers.
• [2] Gemeinder M. (2000): Fuzzy constraint propagation with evolutionary algorithms. - Proc. East West Fuzzy Colloquium, HS Zittau/Görlitz, Germany, pp. 196-203.
• [3] Gemeinder M. (2001a): Restricted density functions for approximate reasoning on distributed quantities. - Proc. 9th Zittau Fuzzy Colloquium, HS Zittau/Görlitz, Germany, pp. 29-35.
• [4] Gemeinder M. (2001B): Computing with words: Multi-objective GAs for approximate reasoning, In: Computational Intelligence, Theory and Applications, Proc. 7th Fuzzy Days, LNCS 2206 (B. Reusch, Ed.) - Berlin: Springer Verlag.
• [5] Hermann M. (2001): Numerische Mathematik. - München: Oldenbourg Wissenschaftsverlag.
• [6] Nissen V. (1997): Einführung in evolutionäre Algorithmen: Optimierung nach dem Vorbild der Evolution. - Braunschweig/Wiesbaden: Vieweg.
• [7] Pohlheim H. (1999): Evolutionäre Algorithmen: Verfahren, Operatoren und Hinweise für die Praxis. - Berlin: Springer Verlag.
• [8] Pozrikidis C. (1998): Numerical Computation in Science and Engineering. - Oxford: Oxford University Press, Inc.
• [9] Zadeh L. A. (1979): A theory of approximate reasoning. - Machine Intell., Vol. 9, pp. 149-194.
• [10] Zadeh L. A. (1999): From computing with numbers to computing with words - From manipulation of measurements to manipulation of perceptions. - IEEE Trans. Circ. Syst., Vol. 45, No. 1, pp. 105-119.
• [11] Zadeh L. A. (2001a): The Robert Example. - BISC Mailinglist, March 2001.
• [12] Zadeh L. A. (2001b): A new direction in AI - Towards a computational theory of perceptions. - 7th Fuzzy Days in Dortmund, Germany, Invited Lecture.