A novel Pythagorean fuzzy PERT approach to measure criticality with multi-criteria in project management problems

In this research article, the credibility distribution is defined as a Pythagorean fuzzy restriction, which serves as an elastic constraint on the possible input states of a variable. This definition relates the credibility theory to the theory of Pythagorean fuzzy sets. The current study first defines Cauchy Pythagorean fuzzy numbers and offers a novel method for precise and analytic determination of the inverse credibility distribution. Examples with various degrees of credibility are shown numerically and graphically. Afterwards, we focus on the identification of critical paths in project networks. For this purpose, Pythagorean fuzzy Logic and Multi-Criteria Decision-Making (MCDM) methodologies are combined in a novel structure that is provided to expand the applications of the project scheduling systems. The development of the Pythagorean Fuzzy Program Evaluation and Review Technique (PFPERT), however, was motivated by the vagueness of the time and cost parameters. The primary objective is to find the critical route while considering some decision criteria such as length, duration, cost, resources, and risk factors. All of the criteria are evaluated mathematically based on Pythagorean fuzzy logic and integrated using the VIKOR approach to obtain the resulting critical route. To further clarify the potentials and capabilities of the suggested strategy, the proposed algorithm is successfully examined for a case study related to a greenhouse construction project.