A New Replacement Model under Trapezoidal Fuzzy Number Environment

Abstract

In today’s dynamic world, the replacement of machinery and facilities is a permanent and complicated issue due to rapid technical growth and globalization, which is a shared concern in the minds of the owners of any business. Maintenance is a scheduled procedure to ensure that equipment, systems, or facilities remain normal to perform their intended purpose correctly without risking the loss of service time due to their failure. To maintain a certain degree of consistency, protection, and performance maintenance activities for systems and facilities in good working conditions are indispensable. The repair operation helps to preserve and increase the operating performance of machinery and facilities and thus adds to revenues. So if an entity or corporation needs to continue its competitive market, it is important to verify if the operating and repair costs are to be sustained with the old equipment or replaced by it. For that, the decision parameters such as maintenance cost, resale value, capital cost, and rate of interest should be known exactly. But it is not possible in reality, as reality is uncertain and complex. This uncertainty is competently governed and controlled by fuzzy set theory. This work aims to discuss equipment replacement in a fuzzy environment. In this fuzzy replacement model, all inaccurate costs are represented by trapezoidal fuzzy numbers (TFNs). The suggested technique finds the best replacement time for a fuzzy replacement problem without converting to a crisp one and is supported by an illustrative numerical example.

Keywords

• Fuzzy Number, Fuzzy replacement model, Midpoint of fuzzy number, Operations on fuzzy numbers, Ranking of fuzzy numbers, Width of fuzzy number