Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

The idea of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and optimization under uncertainty. The activity times in the critical path method (CPM) representation procedures approach are initially static, but in the Project Evaluation and Review Technique (PERT) approach, they are probabilistic. This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy (LDF) environment. The LDF expected task time, LDF variance, LDF critical path, and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network. The primary premise of the LDF-PERT approach is to address ambiguities in project network activity times more simply than other approaches such as conventional PERT, Fuzzy PERT, and so on. The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision. We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings. When the available resources and activity times are imprecise and unpredictable, this strategy can help decision-makers make better judgments in a project. A comparison analysis of the proposed technique with the existing techniques has also been discussed. The suggested techniques are demonstrated with two suitable numerical examples.