Mathematics and Statistics 10(6): 1326-1333, 2022 DOI: 10.13189/ms.2022.100619 http://www.hrpub.org A Study on Intuitionistic Fuzzy Critical Path Problems Through Centroid Based Ranking Method T. Yogashanthi 1 , Shakeela Sathish 1,∗ , K. Ganesan 2 1 Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, 600089, India 2 Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai, 603203, India Received July 30, 2022; Revised October 12, 2022; Accepted October 25, 2022 Cite This Paper in the following Citation Styles (a): [1] T. Yogashanthi, Shakeela Sathish, K. Ganesan, ”A Study on Intuitionistic Fuzzy Critical Path Problems Through Centroid Based Ranking Method,” Mathematics and Statistics, Vol.10, No.6, pp. 1326-1333, 2022. DOI: 10.13189/ms.2022.100619 (b): T. Yogashanthi, Shakeela Sathish, K. Ganesan (2022). A Study on Intuitionistic Fuzzy Critical Path Problems Through Centroid Based Ranking Method. Mathematics and Statistics, 10(6), 1326-1333. DOI: 10.13189/ms.2022.100619 Copyright ©2022 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract In this study the intuitionistic fuzzy version of the critical path method has been proposed to solve network- ing problems with uncertain activity durations. Intuitionistic fuzzy set [1] is an extension of fuzzy set theory [2] unlike fuzzy set, it focuses on degree of belonging, the degree of non- belonging or non-membership function and the degree of hesi- tancy which helps the decision maker to adopt the best among the worst cases. Trapezoidal and the triangular intuitionistic fuzzy numbers are utilized to describe the uncertain activity or task durations of the project network. Here trapezoidal and triangular intuitionistic fuzzy numbers are converted into their corresponding parametric form and applying the proposed in- tuitionistic fuzzy arithmetic operations and a new method of ranking based on the parametric form of intuitionistic fuzzy numbers, the intuitionistic fuzzy critical path with vagueness reduced intuitionistic fuzzy completion duration of the project has been obtained. The authentication of the proposed method can be checked by comparing the obtained results with the re- sults available in pieces of literature. Keywords Trapezoidal Intuitionistic Fuzzy Number, Triangular Intuitionistic Fuzzy Number, Left Fuzziness Index, Right Fuzziness Index, Parametric Form, Intuitionistic Fuzzy Project Duration 1 Introduction In any modern manufacturing system, scheduling plays the most vital role in the production. It helps to plan or design the activities to be implemented in a project and control their progress through a production process. The fundamental principle for all scheduling systems is to create a network of activity and event connections. The main objective of the decision-makers is to optimize the total completion duration of the project and to minimize the project cost. The critical path method is an activity-based method designed for the decision-makers for planning, scheduling and controlling of complicated projects. This method elevates the performance of the project by recognizing critical activities and guides the decision-makers to utilize the available resources properly on these critical activities in the project network and ensures the project quality by minimizing the project cost and time. A project is said to be a successful project only when it meets and satisfies the end-users objectives. However, the critical path method deals with complicated projects more effectively. In a real-world situation, to complete any large and complex project within a minimum time period and getting crisp parameters is impossible due to various real-time causes such as activity delays due to bad weather conditions, materials may not be delivered as planned, etc. Hence, we cannot use the standard method for solving the intuitionistic fuzzy project networking problems. This leads to the development of an intuitionistic fuzzy critical path method as it handles ill known quantities more precisely and considers both degrees of belonging and non-belonging. In 1961, Kelley [3] addressed the importance of critical path method and developed a mathematical proof that includes the essential elements such as time and cost of each project oper- ation. Angelov [4] introduced a new concept to optimization problems with the application of intuitionistic fuzzy sets. Since then, researchers [5][6] were studied and developed many concepts based on intuitionistic fuzzy optimization problems.