zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
General fuzzy linear systems. (English) Zbl 1122.15005
Linear systems $Ax =b$ with fuzzy right-hand side ($b$ and $x$ are vectors of fuzzy numbers) were introduced by {\it M. Friedman, M. Ma} and {\it A. Kandel} [Fuzzy Sets Syst. 96, No. 2, 201--209 (1998); comment and reply ibid. 140, 559--561 (2003; Zbl 0929.15004)], where the method of solutions based on associated $2n \times 2n$ nonnegative matrix $S$ for an $n\times n$ square matrix $A$ and the notions of weak and strong fuzzy solutions was presented. These results are now generalized to the case of an $m \times n$ matrix $A$ by using the generalized inverses of the associated matrix $S$ (in particular the Moore-Penrose inverse). Moreover, in the case of an inconsistent system, the solution of the associated $2m \times 2n$ linear system is replaced by the approximate solution from the least squares method.

15A06Linear equations (linear algebra)
15B48Positive matrices and their generalizations; cones of matrices
15A09Matrix inversion, generalized inverses
08A72Fuzzy algebraic structures
15B33Matrices over special rings (quaternions, finite fields, etc.)
Full Text: DOI
[1] Badard, R.: The law of large numbers for fuzzy processes and the estimation problem. Inform. sci. 28, 161-178 (1982) · Zbl 0588.60004
[2] Tanaka, H.; Uejima, S.; Asai, K.: Linear regression analysis with fuzzy model. IEEE trans. Syst. man cybernet. 12, 903-907 (1982) · Zbl 0501.90060
[3] Buckley, J. J.: Fuzzy eigenvalues and input -- output analysis. Fuzzy sets syst. 34, 187-195 (1990) · Zbl 0687.90021
[4] Friedman, M.; Ming, Ma; Kandel, A.: Fuzzy linear systems. Fuzzy sets syst. 96, 201-209 (1998) · Zbl 0929.15004
[5] Allahviranloo, T.: Numerical methods for fuzzy system of linear equations. Appl. math. Comput. 155, 493-502 (2004) · Zbl 1067.65040
[6] Allahviranloo, T.: Successive over relaxation iterative method for fuzzy system of linear equations. Appl. math. Comput. 162, 189-196 (2005) · Zbl 1062.65037
[7] Babolian, E.; Goghary, H. Sadeghi; Abbasbandy, S.: Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method. Appl. math. Comput. 161, 733-744 (2005) · Zbl 1062.65143
[8] Allahviranloo, T.: The Adomian decomposition method for fuzzy system of linear equations. Appl. math. Comput. 163, 553-563 (2005) · Zbl 1069.65025
[9] Allahviranloo, T.: A comment on fuzzy linear systems. Fuzzy sets syst. 140, 559 (2003) · Zbl 1050.15003
[10] Asady, B.; Abbasbandy, S.; Alavi, M.: Fuzzy general linear systems. Appl. math. Comput. 169, 34-40 (2005) · Zbl 1119.65325
[11] Ben-Israel, A.; Greville, T. N. E.: Generalized inverses: theory and applications. (2003) · Zbl 1026.15004
[12] Plemmons, R. J.: Regular nonnegative matrices. Proc. amer. Math. soc. 39, 26-32 (1973) · Zbl 0273.20051
[13] Berman, A.; Plemmons, R. J.: Nonnegative matrices in the mathematical sciences. (1979) · Zbl 0484.15016