**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30848

##### More on Gaussian Quadratures for Fuzzy Functions

**Authors:**
Shu-Xin Miao

**Abstract:**

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

**Keywords:**
fuzzy number,
fuzzy solution,
Guassian quadrature rules,
fuzzy integral

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1069945

**References:**

[1] J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, second ed., Springer, New York, 1991.

[2] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-352.

[3] L.A. Zadeh, The concept of a linguistic variable and its applications to approximate reasoning, Inform. Sci. 8 (1975) 199-249, 301-357 9 (1975) 43-80.

[4] C-X. Wu, M. Ma, Embedding problem of fuzzy number space: Part I, Fuzzy Sets and Systems 44 (1991) 33-38.

[5] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987) 319-330.

[6] M.L. Puri, D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 409-442.

[7] R. Goetschel, W. Voxman, Elementary calculus, Fuzzy Sets and Systems 18 (1986) 31-43.

[8] T. Allahviranloo, Newton Cot-s methods for integation of fuzzy functions, Applied Mathematics and Computation 166 (2005) 339-348.

[9] T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874- 885.

[10] M. Ma, M. Friedman, A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems 105 (1999) 133-138.

[11] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987) 301-317.

[12] D. Dubois, H. Prade, Towards fuzzy differential calculus, Fuzzy Sets and Systems 8 (1982) 1-7, 105-116, 225-233.

[13] M. Friedman, M. Ma, A. Kandel, Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and Systems 106 (1999) 35-48.

[14] M. Friedman, M. Ma, A. Kandel, Numerical methods for calculating the fuzzy integral, Fuzzy Sets and Systems 83 (1996) 57-62.

[15] S. Abbasbandy, T. Allahviranloo, Numerical solutionof fuzzy differential equation by Talor method, Journal of Computational Method in Applied Mathematics 8 (2002) 43-53.

[16] C.-X. Wu, M. Ma, On embedding problem of fuzzy number spaces, Fuzzy Sets and Systems 44 (1991) 33-38; 45 (1992) 189-202; 46 (1992) 281-286.

[17] J.Y. Park, Y.C. Kwan, J.V. Jeong, Existence of solutions of fuzzy integral equations in Banaeh spaces, Fuzzy Sets and Systems 72 (1995) 373-378.

[18] Byung Soo Moon, A tuning algorithm for the fuzzy logic controllers, EUFIT -95 620-624.

[19] R. Palm, D. Driankov, Fuzzy inputs, Fuzzy Sets and Systems 70 (1995) 315-335.