zbMATH — the first resource for mathematics

Solving systems of linear fuzzy equations. (English) Zbl 0741.65023
Methods for solving a set of fuzzy linear equations are given. The author presents six new solutions and shows that five of these are identical and can be combined. It is shown how these new results are related to the previous research in the area. It is pointed out that the classical solution technique, based on an extension principle and regular fuzzy arithmetic, should be rejected since too often it fails.

65F05 Direct numerical methods for linear systems and matrix inversion
15A06 Linear equations (linear algebraic aspects)
03E72 Theory of fuzzy sets, etc.
Full Text: DOI
[1] Buckley, J.J.; Qu, Y., Solving linear and quadratic fuzzy equations, Fuzzy sets and systems, 38, 43-59, (1990) · Zbl 0713.04004
[2] Buckley, J.J.; Qu, Y., Solving fuzzy equations: a new solution concept, Fuzzy sets and systems, 39, 291-301, (1991) · Zbl 0723.04005
[3] J.J. Buckley, Solving fuzzy equations, J. Math. Anal. Appl., under review. · Zbl 0788.04005
[4] J.J. Buckley and Y. Qu, Fuzzy differential equations: new solutions, J. Math. Anal. Appl., under review. · Zbl 0723.04005
[5] Buckley, J.J.; Qu, Y., On using α-cuts to evaluate fuzzy equations, Fuzzy sets and systems, 38, 309-312, (1990) · Zbl 0723.04006
[6] Hansen, E., Interval arithmetic in matrix computations, part I, SIAM J. numer. anal., 2, 308-320, (1975) · Zbl 0135.37303
[7] Hansen, E., Interval arithmetic in matrix computations, part II, SIAM J. numer. anal., 4, 1-9, (1967) · Zbl 0209.46601
[8] Hansen, E., On the solution of linear algebraic equations with interval coefficients, Linear algebra appl., 2, 153-165, (1969) · Zbl 0185.40201
[9] Jiang, H., The approach to solving the simultaneous linear equations that coefficients are fuzzy numbers, J. nat. univ. defence technol., 3, 93-102, (1986), (in Chinese)
[10] Moore, R.E., Methods and applications of interval analysis, () · Zbl 0302.65047
[11] Weiss, M.D., Fixed points, separation, and induced topologies for fuzzy sets, J. math. anal. appl., 50, 142-150, (1975) · Zbl 0297.54004
[12] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
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.