Steepest descent method for solving fuzzy nonlinear equations

In this paper, we propose the numerical solution for a fuzzy nonlinear equation by steepest descent method. The fuzzy quantities are presented in parametric form. Some numerical illustrations are given to show the efficiency of steepest descent method.

[1]  J. Buckley,et al.  Solving fuzzy equations: a new solution concept , 1991 .

[2]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[3]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[4]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[5]  K. Peeva Fuzzy linear systems , 1992 .

[6]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[7]  H. Carter Fuzzy Sets and Systems — Theory and Applications , 1982 .

[8]  Phil Diamond,et al.  Fuzzy least squares , 1988, Inf. Sci..

[9]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[10]  J. Buckley,et al.  Solving systems of linear fuzzy equations , 1991 .

[11]  James J. Buckley,et al.  On using a-cuts to evaluate fuzzy equations , 1990 .

[12]  Robert Badard,et al.  The law of large numbers for fuzzy processes and the estimation problem , 1982, Inf. Sci..

[13]  J. Miller Numerical Analysis , 1966, Nature.

[14]  Saeid Abbasbandy,et al.  Newton's method for solving fuzzy nonlinear equations , 2004, Appl. Math. Comput..

[15]  J. Buckley,et al.  Solving linear and quadratic fuzzy equations , 1990 .

[16]  Saeid Abbasbandy,et al.  The nearest trapezoidal fuzzy number to a fuzzy quantity , 2004, Appl. Math. Comput..

[17]  Abraham Kandel,et al.  A new fuzzy arithmetic , 1999, Fuzzy Sets Syst..