The cancellation law for pseudo-convolution

Andrea Stupňanová

Kybernetika (2005)

  • Volume: 41, Issue: 3, page [285]-296
  • ISSN: 0023-5954

Abstract

top
Cancellation law for pseudo-convolutions based on triangular norms is discussed. In more details, the cases of extremal t-norms T M and T D , of continuous Archimedean t-norms, and of general continuous t-norms are investigated. Several examples are included.

How to cite

top

Stupňanová, Andrea. "The cancellation law for pseudo-convolution." Kybernetika 41.3 (2005): [285]-296. <http://eudml.org/doc/33754>.

@article{Stupňanová2005,
abstract = {Cancellation law for pseudo-convolutions based on triangular norms is discussed. In more details, the cases of extremal t-norms $T_M$ and $T_D$, of continuous Archimedean t-norms, and of general continuous t-norms are investigated. Several examples are included.},
author = {Stupňanová, Andrea},
journal = {Kybernetika},
keywords = {cancellation law; t-norm; pseudo-convolution; cancellation law; t-norm; pseudo-convolution},
language = {eng},
number = {3},
pages = {[285]-296},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The cancellation law for pseudo-convolution},
url = {http://eudml.org/doc/33754},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Stupňanová, Andrea
TI - The cancellation law for pseudo-convolution
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 3
SP - [285]
EP - 296
AB - Cancellation law for pseudo-convolutions based on triangular norms is discussed. In more details, the cases of extremal t-norms $T_M$ and $T_D$, of continuous Archimedean t-norms, and of general continuous t-norms are investigated. Several examples are included.
LA - eng
KW - cancellation law; t-norm; pseudo-convolution; cancellation law; t-norm; pseudo-convolution
UR - http://eudml.org/doc/33754
ER -

References

top
  1. Baets B. De, Marková-Stupňanová A., 10.1016/S0165-0114(97)00141-3, Fuzzy Sets and Systems 91 (1997), 203–213 (1997) Zbl0919.04005MR1480046DOI10.1016/S0165-0114(97)00141-3
  2. Golan J. S., The Theory of Semirings with Applications in Mathematics and Theoretical Computer Sciences, (Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 54.) Longman, New York 1992 MR1163371
  3. Klement E.-P., Mesiar, R., Pap E., Problems on triangular norms and related operators, Fuzzy Sets and Systems 145 (2004), 471–479 Zbl1050.03019MR2075842
  4. Klement E.-P., Mesiar, R., Pap E., Triangular Norms, (Trends in Logic, Studia Logica Library, Vol. 8.) Kluwer Academic Publishers, Dortrecht 2000 Zbl1087.20041MR1790096
  5. Mareš M., Computation Over Fuzzy Quantities, CRC Press, Boca Raton 1994 Zbl0859.94035MR1327525
  6. Marková A., 10.1016/0165-0114(95)00370-3, Fuzzy Sets and Systems 85 (1997), 379–384 (1997) MR1428314DOI10.1016/0165-0114(95)00370-3
  7. Marková-Stupňanová A., A note on the idempotent functions with respect to pseudo-convolution, Fuzzy Sets and Systems 102 (1999), 417–421 (1999) Zbl0953.28012MR1676908
  8. Mesiar R., 10.1016/0165-0114(95)00401-7, Fuzzy Sets and Systems 86 (1997), 73–78 (1997) Zbl0921.04002MR1438439DOI10.1016/0165-0114(95)00401-7
  9. Mesiar R., 10.1016/S0165-0114(97)00143-7, Fuzzy Sets and Systems 91 (1997), 231–237 (1997) Zbl0919.04011MR1480048DOI10.1016/S0165-0114(97)00143-7
  10. Moynihan R., 10.1007/BF01836553, Aequationes Math. 12 (1975), 2/3, 249–261 (1975) Zbl0309.60013MR0383496DOI10.1007/BF01836553
  11. Murofushi T., Sugeno M., Fuzzy t-conorm integrals with respect to fuzzy measures: generalizations of Sugeno integral and Choquet integral, Fuzzy Sets and Systems 42 (1991), 51–57 (1991) MR1123577
  12. Pap E., 10.1016/S0165-0114(97)00171-1, Fuzzy Sets and Systems 92 (1997), 205–221 (1997) Zbl0934.28015MR1486420DOI10.1016/S0165-0114(97)00171-1
  13. Pap E., Null-Additive Set Functions, Ister Science & Kluwer Academic Publishers, Dordrecht 1995 Zbl1003.28012MR1368630
  14. Pap E., Štajner I., Pseudo-convolution in the theory of optimalization, probabilistic metric spaces, information, fuzzy numbers, system theory, In: Proc. IFSA’97, Praha 1997, pp. 491–495 (1997) 
  15. Pap E., Štajner I., Generalized pseudo-convolution in the theory of probabilistic metric spaces, information, fuzzy numbers, system theory, Fuzzy Sets and Systems 102 (1999), 393–415 (1999) MR1676907
  16. Pap E., Teofanov N., Pseudo-delta sequences, Yugoslav. J. Oper. Res. 8 (1998), 111–128 (1998) MR1621522
  17. Riedel T., 10.1006/jmaa.1994.1207, J. Math. Anal. Appl. 184 (1994), 382–388 (1994) Zbl0802.60022MR1278396DOI10.1006/jmaa.1994.1207
  18. Sugeno M., Murofushi T., 10.1016/0022-247X(87)90354-4, J. Math. Anal. Appl. 122 (1987), 197– 222 (1987) Zbl0611.28010MR0874969DOI10.1016/0022-247X(87)90354-4
  19. Wang Z., Klir G. J., Fuzzy Measure Theory, Plenum Press, New York 1992 Zbl0812.28010MR1212086
  20. Zagrodny D., The cancellation law for inf-convolution of convex functions, Studia Mathematika 110 (1994), 3, 271–282 (1994) Zbl0811.49012MR1292848

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.