Imposing restrictions on density functions utilised in computing with words

Marcus Gemeinder

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 3, page 383-390
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Gemeinder, Marcus. "Imposing restrictions on density functions utilised in computing with words." International Journal of Applied Mathematics and Computer Science 12.3 (2002): 383-390. <http://eudml.org/doc/207595>.

@article{Gemeinder2002,
abstract = {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.},
author = {Gemeinder, Marcus},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {approximate reasoning; computing with words; resemblance; generalised extension principle; generalized extension principle},
language = {eng},
number = {3},
pages = {383-390},
title = {Imposing restrictions on density functions utilised in computing with words},
url = {http://eudml.org/doc/207595},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Gemeinder, Marcus
TI - Imposing restrictions on density functions utilised in computing with words
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 3
SP - 383
EP - 390
AB - 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.
LA - eng
KW - approximate reasoning; computing with words; resemblance; generalised extension principle; generalized extension principle
UR - http://eudml.org/doc/207595
ER -

References

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  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. Zbl1043.68703
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  8. Pozrikidis C. (1998): Numerical Computation in Science and Engineering. - Oxford: Oxford University Press, Inc. Zbl0971.65001
  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. Zbl0954.68513
  11. Zadeh L. A. (2001a): The Robert Example. - BISC Mailing-list, 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. 

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