(untitled) (Contemporary Mathematics, 2024)
Replacement problems involve managing equipment or machines that degrade over time or with usage and those that fail after reaching specific thresholds. Large, expensive assets, such as machine tools and vehicles, have increased maintenance requirements and depreciation over time, raising the risk of obsolescence. The objective is to optimize the replacement and maintenance schedules. This optimization seeks to reduce total costs, which include operating, maintenance and investment expenses. In operations research, effective machine and equipment replacement strategies are critical for sustaining operational efficiency and reducing costs. Abrupt component failures can lead to system-wide disruptions, particularly in digital components like bulbs and resistors. To avoid sudden breakdowns, effective replacement techniques are required. This study compares environments of fuzzy and environments of intuitionistic fuzzy in group replacement and individual replacement approaches. Costs are modeled using triangular and triangular intuitionistic fuzzy numbers to capture uncertainty and vagueness. The research evaluates two strategies: immediate individual replacement and scheduled group replacement. Quantitative and analytical techniques are employed to explore cost uncertainties. Using a centroid-based ranking method, the study assesses outcomes from both fuzzy and intuitionistic fuzzy algorithms to solve complex decision-making scenarios. Results demonstrate that intuitionistic fuzzy approaches offer more effective and optimal outcomes compared to traditional fuzzy methods, enhancing decision-making precision in machine and equipment replacement strategies.