Abstract In an imprecise environment, this article assists organisations or businesses in determining the optimum replacement time and the lowest weighted average cost of machineries. In this article, fuzzy and intuitionistic fuzzy numbers are used to reveal unknown quantities. Practical implementation becomes difficult when numerical values are expressed as unknown quantities, such as intuitionistic fuzzy numbers. Novel approaches to overcoming this computational complexity have been proposed, such as expressing intuitionistic fuzzy numbers into their respective parametric forms involving left fuzziness index, right fuzziness index, and location index of membership and non – membership functions. Arithmetic operations and a centroid-based ranking function are proposed in terms of parametric form. The primary goal of this article is to provide industries with a more precise result so that they can determine the best time to replace machineries or equipment. The original problem’s fuzzy and intuitionistic fuzzy nature is preserved, indicating the proposed work carried out using the proposed arithmetic operations and ranking function. This paper discusses a different solution approach for the replacement problem in a fuzzy environment. This alternative method is used to determine the optimal age of the machine, which we used it to compare the two different machines to determine the best machine among that.

Keywords  Fuzzy optimization, Intuitionistic Triangular fuzzy number, replacement theory