×

On types of fuzzy numbers under addition. (English) Zbl 1249.03095

Summary: We consider the question whether, for given fuzzy numbers, there are different pairs of t-norms such that the resulting membership function with respect to the extension principle under addition are identical. Some examples are given.

MSC:

03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[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 · doi:10.1016/S0165-0114(97)00141-3
[2] Dubois D., Prade H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York 1980 · Zbl 0444.94049
[3] Dubois D., Prade H.: Additions of interactive fuzzy numbers. IEEE Trans. Automat. Control 26 (1981), 926-936 · doi:10.1109/TAC.1981.1102744
[4] Fullér R.: On product sum of triangular fuzzy numbers. Fuzzy Sets and Systems 41 (1991), 83-87 · Zbl 0725.04002 · doi:10.1016/0165-0114(91)90158-M
[5] Fullér R., Keresztfalvi T.: t-norm-based addition of fuzzy intervals. Fuzzy Sets and Systems 51 (1992), 155-159 · Zbl 0875.04008 · doi:10.1016/0165-0114(92)90188-A
[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 · doi:10.1016/0165-0114(92)90017-X
[7] Gebhardt A.: On types of fuzzy numbers and extension principles. Fuzzy Sets and Systems 75 (1995), 311-318 · Zbl 0864.26010 · doi:10.1016/0165-0114(94)00384-J
[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 · doi:10.1016/0165-0114(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 · Zbl 1018.03511 · doi:10.1016/0165-0114(94)90299-2
[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 · doi:10.1016/0165-0114(94)90347-6
[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 · doi:10.1016/S0165-0114(97)00144-9
[12] Hong D. H.: Some results on the addition of fuzzy intervals. Fuzzy Sets and Systems 122 (2001), 349-352 · Zbl 1010.03524 · doi:10.1016/S0165-0114(00)00005-1
[13] Hong D. H.: On shape-preserving additions of fuzzy intervals. J. Math. Anal. Appl. 267 (2002), 369-376 · Zbl 0993.03070 · doi:10.1006/jmaa.2001.7788
[14] Kolesárová A.: Triangular norm-based addition of linear fuzzy numbers. Tatra Mountains Math. Publ. 6 (1995), 75-81 · Zbl 0851.04005
[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
[16] Mareš M., Mesiar R.: Composition of shape generators. Acta Math. Inform. Univ. Ostraviensis 4 (1996), 37-46 · Zbl 0870.04003
[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 · doi:10.1016/S0165-0114(97)00145-0
[18] Marková A.: \(T\)-sum of \(L\)-\(R\) fuzzy numbers. Fuzzy Sets and Systems 85 (1997), 379-384 · Zbl 0904.04007 · doi:10.1016/0165-0114(95)00370-3
[19] Mesiar R.: Triangular norm-based addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 231-237 · Zbl 0919.04011 · doi:10.1016/S0165-0114(97)00143-7
[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 · doi:10.1016/0165-0114(95)00178-6
[21] Mesiar R.: Shape preserving additions of fuzzy intervals. Fuzzy Sets and Systems 86 (1997), 73-78 · Zbl 0921.04002 · doi:10.1016/0165-0114(95)00401-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.