×

zbMATH — the first resource for mathematics

Some results on the addition of fuzzy intervals. (English) Zbl 1010.03524
Summary: A simple new method of computing the \(T\)-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 R. Mesiar [Fuzzy Sets Syst. 91, 231-237 (1997; Zbl 0919.04011)] and A. Marková-Stupnanová [Fuzzy Sets Syst. 91, 253-258 (1997; Zbl 0919.04010)].

MSC:
03E72 Theory of fuzzy sets, etc.
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] De Baets, B.; Mareš, M.; Mesiar, R., \(T\)-partitions of the real line generated by idempotent shapes, Fuzzy sets and systems, 91, 177-184, (1997) · Zbl 0919.04004
[2] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE trans. automat. control, 26, 926-936, (1981)
[3] Fullér, R., On product sum of triangular fuzzy numbers, Fuzzy sets and systems, 41, 83-87, (1991) · Zbl 0725.04002
[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 numbers, Fuzzy sets and systems, 66, 381-382, (1994) · Zbl 0844.04005
[7] Hong, D.H.; Hwang, S.Y., On the compositional rule of inference under triangular norms, Fuzzy sets and systems, 66, 24-38, (1994) · Zbl 1018.03511
[8] 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
[9] Hong, D.H.; Hwang, C., A \(T\)-sum bound of \(LR\)-fuzzy numbers, Fuzzy sets and systems, 91, 239-252, (1997) · Zbl 0920.04010
[10] Kolesárová, A., Triangular norm-based addition of linear fuzzy numbers, Tatra moutains math. publ., 6, 75-81, (1995) · Zbl 0851.04005
[11] Kolesárová, A., Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals, Mathware soft computing, 5, 91-98, (1998) · Zbl 0934.03064
[12] Mareš, M.; Mesiar, R., Composition of shape generators, Acta math. inform. univ. ostraviensis, 4, 37-46, (1996) · Zbl 0870.04003
[13] Marková, A., A note to the addition of fuzzy numbers based on a continuous Archimedean t-norm, Fuzzy sets and systems, 91, 253-258, (1997) · Zbl 0919.04010
[14] Marková, A., \(T\)-sum of \(L\)-\(R\) fuzzy numbers, Fuzzy sets and systems, 85, 379-384, (1997) · Zbl 0904.04007
[15] Mesiar, R., A note to the \(T\)-sum of \(L\)-\(R\) fuzzy numbers, Fuzzy sets and systems, 87, 259-261, (1996) · Zbl 0871.04010
[16] Mesiar, R., Shape preserving additions of fuzzy intervals, Fuzzy sets and systems, 86, 73-78, (1997) · Zbl 0921.04002
[17] Mesiar, R., Triangular norm-based addition of fuzzy intervals, Fuzzy sets and systems, 91, 231-237, (1997) · Zbl 0919.04011
[18] Schweizer, B.; Sklar, A., Associative functions and abstract semigroups, Publ. math. debrecen, 10, 69-81, (1963) · Zbl 0119.14001
[19] Triescsh, E., Characterisation of Archimedian t-norms and a law of large numbers, Fuzzy sets and systems, 58, 189-192, (1993)
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.