Title: Solution of a mining equipment maintenance system model in imprecise environment

Authors: Ashok Kumar Shaw; Mostafijur Rahaman; Sankar Prasad Mondal; Banashree Chatterjee; Shariful Alam

Addresses: Department of Mathematics, Regent Education and Research Foundation, Bara Kanthalia, Sewli Telini Para, North 24 Parganas, Barrackpore, Kolkata, West Bengal, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India ' Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, India ' Department of Information Technology, Dr. B.C. Roy Engineering College, Durgapur, West Bengal, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India

Abstract: In this paper, a mining equipment maintenance system is depicted by a mathematical model described in terms of a pair of differential equations. The impreciseness involved in a real-life situation is accounted in this paper letting the initial condition and associated parameters to be imprecise in nature. Two most popular mathematical knowledge dealing with the sense of uncertainty, namely the fuzzy and interval environments are utilised here to analyse and solve the proposed model under uncertainty. The solutions of the uncertain differential equations (both interval and fuzzy) corresponding to the model are getting inspired by the generalised Hukuhara derivative of a set valued function. Different crispification techniques of converting the fuzzy and interval solutions into their crisp representatives are manifested to compute and compare the score of feasible decisions under uncertainty.

Keywords: mining equipment maintenance problem; generalised Hukuhara derivative; fuzzy differential equation; FDE; interval differential equation; removal area method; mean of centre method.

DOI: 10.1504/IJOR.2024.143342

International Journal of Operational Research, 2024 Vol.51 No.4, pp.562 - 598

Received: 22 May 2021
Accepted: 02 Nov 2021
Published online: 16 Dec 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article