| Title:
             | 
A note about operations like $T_W$ (the weakest $t$-norm) based addition on fuzzy intervals (English) | 
| Author:
             | 
Hong, Dug Hun | 
| Language:
             | 
English | 
| Journal:
             | 
Kybernetika | 
| ISSN:
             | 
0023-5954 | 
| Volume:
             | 
45 | 
| Issue:
             | 
3 | 
| Year:
             | 
2009 | 
| Pages:
             | 
541-547 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous $t$-norms to act as the weakest $t$-norm $T_W$-based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18]. (English) | 
| Keyword:
             | 
fuzzy arithmetics | 
| Keyword:
             | 
fuzzy intervals | 
| Keyword:
             | 
triangular norms | 
| MSC:
             | 
03E72 | 
| MSC:
             | 
62A10 | 
| MSC:
             | 
62A86 | 
| MSC:
             | 
62F15 | 
| MSC:
             | 
93E12 | 
| idZBL:
             | 
Zbl 1165.93340 | 
| idMR:
             | 
MR2543139 | 
| . | 
| Date available:
             | 
2010-06-02T18:49:04Z | 
| Last updated:
             | 
2012-06-06 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/140012 | 
| . | 
| Reference:
             | 
[1] D. Dubois and H. Prade: Additions of interactive fuzzy numbers.IEEE Trans. Automat. Control 26 (1981), 926–936. MR 0635852 | 
| Reference:
             | 
[2] R. Fullér and T. Keresztfalvi: $t$-norm-based addition of fuzzy intervals.Fuzzy Sets and Systems 51 (1992), 155–159. MR 1188307 | 
| Reference:
             | 
[3] D. H. Hong and S. Y. Hwang: The convergence of $T$-product of fuzzy numbers.Fuzzy Sets and Systems 85 (1997), 373–378. MR 1428313 | 
| Reference:
             | 
[4] D. H. Hong: A note on $t$-norm-based addition of fuzzy intervals.Fuzzy Sets and Systems 75 (1995), 73–76. Zbl 0947.26024, MR 1351592 | 
| Reference:
             | 
[5] D. H. Hong and C. Hwang: A $T$-sum bound of $LR$-fuzzy numbers.Fuzzy Sets and Systems 91 (1997), 239–252. MR 1480049 | 
| Reference:
             | 
[6] D. H. Hong and H. Kim: A note to the sum of fuzzy variables.Fuzzy Sets and Systems 93 (1998), 121–124. MR 1601517 | 
| Reference:
             | 
[7] D. H. Hong and S. Y. Hwang: On the compositional rule of inference under triangular norms.Fuzzy Sets and Systems 66 (1994), 25–38. MR 1294689 | 
| Reference:
             | 
[8] D. H. Hong: Shape preserving multiplications of fuzzy intervals.Fuzzy Sets and Systems 123 (2001), 93–96. MR 1848797 | 
| Reference:
             | 
[9] D. H. Hong: Some results on the addition of fuzzy intervals.Fuzzy Sets and Systems 122 (2001), 349–352. Zbl 1010.03524, MR 1854823 | 
| Reference:
             | 
[10] D. H. Hong: On shape-preserving additions of fuzzy intervals.J. Math. Anal. Appl. 267 (2002), 369–376. Zbl 0993.03070, MR 1886835 | 
| Reference:
             | 
[11] T. Keresztfalvi and M. Kovács: $g, p$-fuzzification of arithmetic operations.Tatra Mountains Math. Publ. 1 (1992), 65–71. MR 1230464 | 
| Reference:
             | 
[12] A. Kolesárová: Triangular norm-based addition preserving linearity of $t$-sums of fuzzy intervals.Mathware and Soft Computing 5 (1998), 97–98. MR 1632755 | 
| Reference:
             | 
[13] A. Kolesárová: Triangular norm-based addition of linear fuzzy numbers.Tatra Mountains Math. Publ. 6 (1995), 75–82. MR 1363985 | 
| Reference:
             | 
[14] A. Marková: $T$-sum of $L$-$R$-fuzzy numbers.Fuzzy Sets and Systems 85 (1996), 379–384. MR 1428314 | 
| Reference:
             | 
[15] A. Marková–Stupňanová: A note to the addition of fuzzy numbers based on a continuous Archimedean $T$-norm.Fuzzy Sets and Systems 91 (1997), 253–258. | 
| Reference:
             | 
[16] R. Mesiar: A note on the $T$-sum of $LR$ fuzzy numbers.Fuzzy Sets and Systems 79 (1996), 259–261. MR 1388398 | 
| Reference:
             | 
[17] R. Mesiar: Shape preserving additions of fuzzy intervals.Fuzzy Sets and Systems 86 (1997), 73–78. Zbl 0921.04002, MR 1438439 | 
| Reference:
             | 
[18] R. Mesiar: Triangular-norm-based addition of fuzzy intervals.Fuzzy Sets and Systems 91 (1997), 231–237. Zbl 0919.04011, MR 1480048 | 
| Reference:
             | 
[19] B. Schweizer and A. Star: Associative functions and abstract semigroups.Publ. Math. Debrecen 10 (1963), 69–81. MR 0170967 | 
| Reference:
             | 
[20] L. A. Zadeh: The concept of a linguistic variable and its applications to approximate reasoning, Parts, I, II, III.Inform. Sci. 8 (1975), 199–251, 301–357; 9 (1975) 43–80. | 
| . |