A novel approach for solving fuzzy differential equations using Runge-Kutta and Biogeography-based optimization

Article type: Research Article

Authors: Garg, Harish^*

Affiliations: School of Mathematics, Thapar University Patiala, Punjab, India

Correspondence: [*] Corresponding author. Harish Garg, School of Mathematics, Thapar University Patiala-147004, Punjab, India. Tel.: +918699031147; E-mail: [email protected]; Url: http://sites.google.com/site/harishg58iitr/.

Abstract: The objective of this work is to present a methodology for solving the Kolmogorov’s differential equations in fuzzy environment using Runga-Kutta and Biogeography-based optimization (RKBBO) algorithm. As most of the data are usually uncertain and hence the fuzzy set theory has been used for handling the uncertainties and therefore the corresponding differential equations becomes fuzzy Kolmogorov’s differential equations. The obtained differential equations has been solved by Runga-Kutta method and improvement of their solution has been found by formulating a nonlinear optimization problem and solved by BBO for finding the global or near to global solutions. Performance index has been used for finding the most critical component of the system for increasing the performance of system by considering reliability, availability and maintainability index. Final results are compared with the existing results. To show the application of the proposed method, a case of the thermal power plant, a repairable industrial system, has been taken for evaluating the fuzzy reliability of the system.

Keywords: Biogeography-based optimization, Runge-Kutta method, differential equation, fuzzy numbers, reliability, repairable system

DOI: 10.3233/IFS-152010

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2417-2429, 2016