On types of fuzzy numbers under addition

Dug Hun Hong

Kybernetika (2004)

  • Volume: 40, Issue: 4, page [469]-476
  • ISSN: 0023-5954

Abstract

top
We consider the question whether, for given fuzzy numbers, there are different pairs of t -norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.

How to cite

top

Hong, Dug Hun. "On types of fuzzy numbers under addition." Kybernetika 40.4 (2004): [469]-476. <http://eudml.org/doc/33712>.

@article{Hong2004,
abstract = {We consider the question whether, for given fuzzy numbers, there are different pairs of $t$-norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.},
author = {Hong, Dug Hun},
journal = {Kybernetika},
keywords = {fuzzy number; extension principles; $t$-norms; fuzzy number; extension principles; t-norm},
language = {eng},
number = {4},
pages = {[469]-476},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On types of fuzzy numbers under addition},
url = {http://eudml.org/doc/33712},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Hong, Dug Hun
TI - On types of fuzzy numbers under addition
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 4
SP - [469]
EP - 476
AB - We consider the question whether, for given fuzzy numbers, there are different pairs of $t$-norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.
LA - eng
KW - fuzzy number; extension principles; $t$-norms; fuzzy number; extension principles; t-norm
UR - http://eudml.org/doc/33712
ER -

References

top
  1. Baets B. D., 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. Dubois D., Prade H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York 1980 Zbl0444.94049MR0589341
  3. Dubois D., Prade H., 10.1109/TAC.1981.1102744, IEEE Trans. Automat. Control 26 (1981), 926–936 (1981) MR0635852DOI10.1109/TAC.1981.1102744
  4. Fullér R., 10.1016/0165-0114(91)90158-M, Fuzzy Sets and Systems 41 (1991), 83–87 (1991) Zbl0725.04002MR1104983DOI10.1016/0165-0114(91)90158-M
  5. Fullér R., Keresztfalvi T., 10.1016/0165-0114(92)90188-A, Fuzzy Sets and Systems 51 (1992), 155–159 (1992) MR1188307DOI10.1016/0165-0114(92)90188-A
  6. Fullér R., Zimmermann H. J., 10.1016/0165-0114(92)90017-X, Fuzzy Sets and Systems 51 (1992), 267–275 (1992) Zbl0782.68110MR1192447DOI10.1016/0165-0114(92)90017-X
  7. Gebhardt A., 10.1016/0165-0114(94)00384-J, Fuzzy Sets and Systems 75 (1995), 311–318 (1995) Zbl0864.26010MR1358717DOI10.1016/0165-0114(94)00384-J
  8. Hong D. H., 10.1016/0165-0114(94)90106-6, Fuzzy Sets and Systems 66 (1994), 381–382 (1994) Zbl0844.04005MR1300295DOI10.1016/0165-0114(94)90106-6
  9. Hong D. H., Hwang S. Y., On the compositional rule of inference under triangular norms, Fuzzy Sets and Systems 66 (1994), 24–38 (1994) Zbl1018.03511MR1294689
  10. Hong D. H., Hwang S. Y., 10.1016/0165-0114(94)90347-6, Fuzzy Sets and Systems 63 (1994), 175–180 (1994) Zbl0844.04004MR1275891DOI10.1016/0165-0114(94)90347-6
  11. Hong D. H., Hwang C., 10.1016/S0165-0114(97)00144-9, Fuzzy Sets and Systems 91 (1997), 239–252 (1997) Zbl0920.04010MR1480049DOI10.1016/S0165-0114(97)00144-9
  12. Hong D. H., 10.1016/S0165-0114(00)00005-1, Fuzzy Sets and Systems 122 (2001), 349–352 Zbl1010.03524MR1854823DOI10.1016/S0165-0114(00)00005-1
  13. Hong D. H., 10.1006/jmaa.2001.7788, J. Math. Anal. Appl. 267 (2002), 369–376 Zbl0993.03070MR1886835DOI10.1006/jmaa.2001.7788
  14. Kolesárová A., Triangular norm-based addition of linear fuzzy numbers, Tatra Mountains Math. Publ. 6 (1995), 75–81 (1995) Zbl0851.04005MR1363985
  15. Kolesárová K., Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals, Mathware and Soft Computing 5 (1998), 91–98 (1998) Zbl0934.03064MR1632755
  16. Mareš M., Mesiar R., Composition of shape generators, Acta Math. Inform. Univ. Ostraviensis 4 (1996), 37–46 (1996) Zbl0870.04003MR1446782
  17. Marková–Stupňanová A., A note to the addition of fuzzy numbers based on a continuous Archimedean t -norm, Fuzzy Sets and Systems 91 (1997), 253–258 (1997) Zbl0919.04010
  18. 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
  19. 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
  20. Mesiar R., 10.1016/0165-0114(95)00178-6, Fuzzy Sets and Systems 87 (1996), 259–261 (1996) Zbl0871.04010MR1388398DOI10.1016/0165-0114(95)00178-6
  21. 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

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.