Error estimation of ‎f‎uzzy Newton-Cotes method for Integration of fuzzy functions‎

Subject Areas : International Journal of Industrial Mathematics

N. Ahmady ¹ , E. Ahmady ²

1 - Department of Mathematics, Varamin-Pishva Branch, Islamic Azad University, Varamin, Iran.
2 - Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran.

Received: 2016-01-23 Accepted : 2016-01-23 Published : 2016-01-01

Keywords: Fuzzy integration, ‎F‎uzzy Newton-Cotes method, Fuzzy trapezoidal's rule, Fuzzy Simpson's ‎rule,

Abstract :

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and fuzzy Simpson rule is accurate for polynomial of degree three. The accuracy of fuzzy Trapezoidal rule and fuzzy Simpson rule for integration of fuzzy functions are illustrated by two ‎examples.‎