Some results on the addition of fuzzy intervals

Abstract A simple new method of computing T -sum of fuzzy intervals having the same results as the sum of fuzzy intervals based on the weakest t-norm T W is introduced. This work extends that of Mesiar [Fuzzy Sets and Systems 91 (1997) 231–237] and Markova [Fuzzy Sets and Systems 91 (1997) 253–258].

[1]  Radko Mesiar A note to the T-sum of L-R fuzzy numbers , 1996, Fuzzy Sets Syst..

[2]  D. Hong,et al.  On the compositional rule of inference under triangular norms , 1994 .

[3]  Andrea Marková-Stupňanová A note to the addition of fuzzy numbers based on a continuous Archimedean T-norm , 1997 .

[4]  E. Triesch Characterisation of Archimedian t -norms and a law of large numbers , 1993 .

[5]  R. Fullér On product-sum of triangular fuzzy numbers , 1991 .

[6]  Dug Hun Hong,et al.  On the convergence of T-sum of L-R fuzzy numbers , 1994 .

[7]  Dug Hun Hong,et al.  A note on product-sum of L–R fuzzy numbers , 1994 .

[8]  Radko Mesiar,et al.  Triangular-norm-based addition of fuzzy intervals , 1997, Fuzzy Sets Syst..

[9]  Radko Mesiar,et al.  Shape preserving additions of fuzzy intervals , 1997, Fuzzy Sets Syst..

[10]  Tibor Keresztfalvi,et al.  t-Norm-based addition of fuzzy intervals , 1992 .

[11]  Radko Mesiar,et al.  Τ-partitions of the Real Line Generated by Idempotent Shapes , 1997, Fuzzy Sets Syst..

[12]  Dug Hun Hong,et al.  A T-sum bound of LR-fuzzy numbers , 1997, Fuzzy Sets Syst..

[13]  D. Dubois,et al.  Additions of interactive fuzzy numbers , 1981 .

[14]  Andrea Stupnanová A note to the addition of fuzzy numbers based on a continuous Archimedean T-norm , 1997, Fuzzy Sets Syst..

[15]  H. Zimmermann,et al.  On computation of the compositional rule of inference under triangular norms , 1992 .

[16]  Anna Kolesárová Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals , 1998 .

[17]  Andrea Marková T-sum of L-R fuzzy numbers , 1997, Fuzzy Sets Syst..