# Article

Full entry | PDF   (1.1 MB)
Keywords:
cancellation law; t-norm; pseudo-convolution
Summary:
Cancellation law for pseudo-convolutions based on triangular norms is discussed. In more details, the cases of extremal t-norms $T_M$ and $T_D$, of continuous Archimedean t-norms, and of general continuous t-norms are investigated. Several examples are included.
References:
[1] Baets B. De, Marková-Stupňanová A.: Analytical expressions for the addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 203–213 MR 1480046 | Zbl 0919.04005
[2] Golan J. S.: The Theory of Semirings with Applications in Mathematics and Theoretical Computer Sciences. (Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 54.) Longman, New York 1992 MR 1163371
[3] Klement E.-P., Mesiar, R., Pap E.: Problems on triangular norms and related operators. Fuzzy Sets and Systems 145 (2004), 471–479 MR 2075842 | Zbl 1050.03019
[4] Klement E.-P., Mesiar, R., Pap E.: Triangular Norms. (Trends in Logic, Studia Logica Library, Vol. 8.) Kluwer Academic Publishers, Dortrecht 2000 MR 1790096 | Zbl 1087.20041
[5] Mareš M.: Computation Over Fuzzy Quantities. CRC Press, Boca Raton 1994 MR 1327525 | Zbl 0859.94035
[6] Marková A.: T-sum of L-R fuzzy numbers. Fuzzy Sets and Systems 85 (1997), 379–384 MR 1428314
[7] Marková-Stupňanová A.: A note on the idempotent functions with respect to pseudo-convolution. Fuzzy Sets and Systems 102 (1999), 417–421 MR 1676908 | Zbl 0953.28012
[8] Mesiar R.: Shape preserving additions of fuzzy intervals. Fuzzy Sets and Systems 86 (1997), 73–78 MR 1438439 | Zbl 0921.04002
[9] Mesiar R.: Triangular-norm-based addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 231–237 MR 1480048 | Zbl 0919.04011
[10] Moynihan R.: On the class of $\tau _T$ semigroups of probability distribution functions. Aequationes Math. 12 (1975), 2/3, 249–261 MR 0383496 | Zbl 0309.60013
[11] Murofushi T., Sugeno M. : Fuzzy t-conorm integrals with respect to fuzzy measures: generalizations of Sugeno integral and Choquet integral. Fuzzy Sets and Systems 42 (1991), 51–57 MR 1123577
[12] Pap E.: Decomposable measures and nonlinear equations. Fuzzy Sets and Systems 92 (1997), 205–221 MR 1486420 | Zbl 0934.28015
[13] Pap E.: Null-Additive Set Functions. Ister Science & Kluwer Academic Publishers, Dordrecht 1995 MR 1368630 | Zbl 1003.28012
[14] Pap E., Štajner I.: Pseudo-convolution in the theory of optimalization, probabilistic metric spaces, information, fuzzy numbers, system theory. In: Proc. IFSA’97, Praha 1997, pp. 491–495
[15] Pap E., Štajner I.: Generalized pseudo-convolution in the theory of probabilistic metric spaces, information, fuzzy numbers, system theory. Fuzzy Sets and Systems 102 (1999), 393–415 MR 1676907
[16] Pap E., Teofanov N.: Pseudo-delta sequences. Yugoslav. J. Oper. Res. 8 (1998), 111–128 MR 1621522
[17] Riedel T.: On $\sup$-continuous triangle functions. J. Math. Anal. Appl. 184 (1994), 382–388 MR 1278396 | Zbl 0802.60022
[18] Sugeno M. , Murofushi T.: Pseudo-additive measures and integrals. J. Math. Anal. Appl. 122 (1987), 197– 222 MR 0874969 | Zbl 0611.28010
[19] Wang Z., Klir G. J.: Fuzzy Measure Theory. Plenum Press, New York 1992 MR 1212086 | Zbl 0812.28010
[20] Zagrodny D.: The cancellation law for inf-convolution of convex functions. Studia Mathematika 110 (1994), 3, 271–282 MR 1292848 | Zbl 0811.49012

Partner of