×
Marková, Andrea

\(T\)-sums of L-R fuzzy numbers. (English) Zbl 0904.04007

Fuzzy Sets Syst. 85, No. 3, 379-384 (1997).
Summary: The sum of L-R fuzzy numbers based on a given Archimedian continuous \(t\)-norm \(T\) is studied. A series of sufficient conditions improving those of several authors and ensuring an analytical form of the output sum is completed by a sufficient and necessary condition, i.e., the best sufficient condition. Some applications are indicated.

Cited in 2 Reviews
Cited in 25 Documents

MSC:

03E72 Theory of fuzzy sets, etc.

Keywords:

Archimedean \(t\)-norm; extension principle; triangular norms; \(T\)-sum; L-R fuzzy numbers
PDF BibTeX XML Cite
\textit{A. Marková}, Fuzzy Sets Syst. 85, No. 3, 379--384 (1997; Zbl 0904.04007)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE Trans. Automat. Control, 26, 926-936 (1981) · Zbl 1457.68262
[2] Fullér, R., On product-sum of triangular fuzzy numbers, Fuzzy Sets and Systems, 41, 83-87 (1991) · Zbl 0725.04002
[3] Fullér, R., A law of large numbers for fuzzy numbers, Fuzzy Sets and Systems, 45, 299-303 (1992) · Zbl 0748.60003
[4] Fullér, R.; Keresztfalvi, T., t-norm-based addition of fuzzy intervals, Fuzzy Sets and Systems, 51, 155-159 (1992)
[5] Fullér, R.; Zimmermann, H. J., On computation of the compositional rule of inference under triangular norms, Fuzzy Sets and Systems, 51, 267-275 (1992) · Zbl 0782.68110
[6] Hong, D. H., A note on product-sum of \(L-R\) fuzzy, Fuzzy Sets and Systems, 66, 381-382 (1994) · Zbl 0844.04005
[7] Hong, D. H., A note on the law of large numbers for fuzzy numbers, Fuzzy Sets and Systems, 64, 59-61 (1994) · Zbl 0848.60004
[8] Hong, D. H.; Hwang, S. Y., On the compositional rule of inference under triangular norms, Fuzzy Sets and Systems, 66, 25-38 (1994) · Zbl 1018.03511
[9] Hong, D. H.; Hwang, S. Y., On the convergence of \(T\)-sum of \(L-R\) fuzzy numbers, Fuzzy Sets and Systems, 63, 175-180 (1994) · Zbl 0844.04004
[10] Klement, E. P., Integration of fuzzy valued functions, Revue Roumain Math. Pures Appl., 30, 375-384 (1985) · Zbl 0611.28009
[11] Kolesárová, A., Triangular norm — based addition of linear fuzzy numbers, Tatra Mountains Math. Publ., 6, 75-81 (1995) · Zbl 0851.04005
[12] Mareš, M., Computation over Fuzzy Quantities (1994), CRC Press: CRC Press Boca Raton, FL · Zbl 0859.94035
[13] Marková, A., Additions of \(L-R\) fuzzy numbers, Busefal, 63, 25-29 (1995)
[14] Mesiar, R., A note on the \(T\)-sum of \(L-R\) fuzzy numbers, Fuzzy Sets and Systems, 79, 259-261 (1996) · Zbl 0871.04010
[15] Mesiar, R., Shape preserving additions of fuzzy intervals, 86, 75-80 (1997)
[16] Mesiar, R., Computation over LR-fuzzy numbers, (Proc. CIFT’95. Proc. CIFT’95, Trento (1995)), 165-176
[17] Triesch, E., On the convergence of product-sum series of \(L-R\) fuzzy numbers, Fuzzy Sets and Systems, 53, 189-192 (1993) · Zbl 0874.26019
[18] Triesch, E., Characterisation of Archimedian t-norms and a law of large numbers, Fuzzy Sets and Systems, 58, 339-342 (1993) · Zbl 0788.60041
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.