| Title:
|
On types of fuzzy numbers under addition (English) |
| Author:
|
Hong, Dug Hun |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
[469]-476 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
fuzzy number |
| Keyword:
|
extension principles |
| Keyword:
|
$t$-norms |
| MSC:
|
03E20 |
| MSC:
|
03E72 |
| idZBL:
|
Zbl 1249.03095 |
| idMR:
|
MR2102365 |
| . |
| Date available:
|
2009-09-24T20:02:51Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135608 |
| . |
| Reference:
|
[1] Baets B. D., Marková–Stupňanová A.: Analytical expressions for the addition of fuzzy intervals.Fuzzy Sets and Systems 91 (1997), 203–213 Zbl 0919.04005, MR 1480046, 10.1016/S0165-0114(97)00141-3 |
| Reference:
|
[2] Dubois D., Prade H.: Fuzzy Sets and Systems: Theory and Applications.Academic Press, New York 1980 Zbl 0444.94049, MR 0589341 |
| Reference:
|
[3] Dubois D., Prade H.: Additions of interactive fuzzy numbers.IEEE Trans. Automat. Control 26 (1981), 926–936 MR 0635852, 10.1109/TAC.1981.1102744 |
| Reference:
|
[4] Fullér R.: On product sum of triangular fuzzy numbers.Fuzzy Sets and Systems 41 (1991), 83–87 Zbl 0725.04002, MR 1104983, 10.1016/0165-0114(91)90158-M |
| Reference:
|
[5] Fullér R., Keresztfalvi T.: t-norm-based addition of fuzzy intervals.Fuzzy Sets and Systems 51 (1992), 155–159 MR 1188307, 10.1016/0165-0114(92)90188-A |
| Reference:
|
[6] Fullér R., Zimmermann H. J.: On computation of the compositional rule of inference under triangular norms.Fuzzy Sets and Systems 51 (1992), 267–275 Zbl 0782.68110, MR 1192447, 10.1016/0165-0114(92)90017-X |
| Reference:
|
[7] Gebhardt A.: On types of fuzzy numbers and extension principles.Fuzzy Sets and Systems 75 (1995), 311–318 Zbl 0864.26010, MR 1358717, 10.1016/0165-0114(94)00384-J |
| Reference:
|
[8] Hong D. H.: A note on product-sum of $L$-$R$ fuzzy numbers.Fuzzy Sets and Systems 66 (1994), 381–382 Zbl 0844.04005, MR 1300295, 10.1016/0165-0114(94)90106-6 |
| Reference:
|
[9] Hong D. H., Hwang S. Y.: On the compositional rule of inference under triangular norms.Fuzzy Sets and Systems 66 (1994), 24–38 Zbl 1018.03511, MR 1294689 |
| Reference:
|
[10] Hong D. H., Hwang S. Y.: On the convergence of $T$-sum of $L$-$R$ fuzzy numbers.Fuzzy Sets and Systems 63 (1994), 175–180 Zbl 0844.04004, MR 1275891, 10.1016/0165-0114(94)90347-6 |
| Reference:
|
[11] Hong D. H., Hwang C.: A $T$-sum bound of $LR$-fuzzy numbers.Fuzzy Sets and Systems 91 (1997), 239–252 Zbl 0920.04010, MR 1480049, 10.1016/S0165-0114(97)00144-9 |
| Reference:
|
[12] Hong D. H.: Some results on the addition of fuzzy intervals.Fuzzy Sets and Systems 122 (2001), 349–352 Zbl 1010.03524, MR 1854823, 10.1016/S0165-0114(00)00005-1 |
| Reference:
|
[13] Hong D. H.: On shape-preserving additions of fuzzy intervals.J. Math. Anal. Appl. 267 (2002), 369–376 Zbl 0993.03070, MR 1886835, 10.1006/jmaa.2001.7788 |
| Reference:
|
[14] Kolesárová A.: Triangular norm-based addition of linear fuzzy numbers.Tatra Mountains Math. Publ. 6 (1995), 75–81 Zbl 0851.04005, MR 1363985 |
| Reference:
|
[15] Kolesárová K.: Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals.Mathware and Soft Computing 5 (1998), 91–98 Zbl 0934.03064, MR 1632755 |
| Reference:
|
[16] Mareš M., Mesiar R.: Composition of shape generators.Acta Math. Inform. Univ. Ostraviensis 4 (1996), 37–46 Zbl 0870.04003, MR 1446782 |
| Reference:
|
[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 Zbl 0919.04010 |
| Reference:
|
[18] Marková A.: $T$-sum of $L$-$R$ fuzzy numbers.Fuzzy Sets and Systems 85 (1997), 379–384 MR 1428314, 10.1016/0165-0114(95)00370-3 |
| Reference:
|
[19] Mesiar R.: Triangular norm-based addition of fuzzy intervals.Fuzzy Sets and Systems 91 (1997), 231–237 Zbl 0919.04011, MR 1480048, 10.1016/S0165-0114(97)00143-7 |
| Reference:
|
[20] Mesiar R.: A note to the $T$-sum of $L$-$R$ fuzzy numbers.Fuzzy Sets and Systems 87 (1996), 259–261 Zbl 0871.04010, MR 1388398, 10.1016/0165-0114(95)00178-6 |
| Reference:
|
[21] Mesiar R.: Shape preserving additions of fuzzy intervals.Fuzzy Sets and Systems 86 (1997), 73–78 Zbl 0921.04002, MR 1438439, 10.1016/0165-0114(95)00401-7 |
| . |
