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Keywords:
$t$-norm; law of large numbers for fuzzy numbers
$t$-norm; law of large numbers for fuzzy numbers
Summary:
The notions of a $t$-norm and of a fuzzy number are recalled. The law of large numbers for fuzzy numbers is defined. The fuzzy numbers, for which the law of large numbers holds, are investigated. The case when the law of large numbers is violated is studied.
References:
[1] Baets B. de, Stupňanová A. Marková –: Analytical expressions for the addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 203–213 DOI 10.1016/S0165-0114(97)00141-3 | MR 1480046
[2] Fullér R.: A law of large numbers for fuzzy numbers. Fuzzy Sets and Systems 45 (1992), 299–303 DOI 10.1016/0165-0114(92)90147-V | MR 1154193 | Zbl 0748.60003
[3] Hong D. H.: A note on the law of large numbers for fuzzy numbers. Fuzzy Sets and Systems 68 (1994), 243 MR 1321502 | Zbl 0848.60005
[4] Hong D. H.: A convergence theorem for array of $L$-$R$ fuzzy numbers. Inform. Sci. 88 (1996), 169–175 DOI 10.1016/0020-0255(95)00160-3 | MR 1375365
[5] Kolesárová A.: Triangular norm–based addition of linear fuzzy numbers. Tatra Mountains Math. Publ. 6 (1995), 75–81 MR 1363985 | Zbl 0851.04005
[6] Kolesárová A.: Triangular norm–based addition preserving the linearity of $T$-sums of linear fuzzy intervals. Mathware and Soft Computing 5 (1998), 91–98 MR 1632755
[7] Marková A.: $T$-sums of $L$-$R$ fuzzy numbers. Fuzzy Sets and Systems 85 (1997), 379–384 DOI 10.1016/0165-0114(95)00370-3 | MR 1428314 | Zbl 0904.04007
[8] Stupňanová A. Marková –: The law of large numbers. Busefal 75 (1998), 53–59
[9] Stupňanová A. Marková –: A note on recent results on the law of large numbers for fuzzy numbers. Busefal 76 (1998), 12–18
[10] Mesiar R.: A note to the $T$-sum of $L$-$R$ fuzzy numbers. Fuzzy Sets and Systems 79 (1996), 259–261 DOI 10.1016/0165-0114(95)00178-6 | MR 1388398 | Zbl 0871.04010
[11] Mesiar R.: Shape preserving additions of fuzzy intervals. Fuzzy Sets and Systems 86 (1996), 73–78 DOI 10.1016/0165-0114(95)00401-7 | MR 1438439
[12] Mesiar R.: Triangular–norm–based addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1996), 231–237 DOI 10.1016/S0165-0114(97)00143-7 | MR 1480048
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