Context: Nowadays, companies are investing in brand new software, given that fact they always need help with estimating software development, effort, costs, and the period of time needed for completing the software itself. In this paper, four different architectures of Artificial Neural Networks (ANN), as one of the most desired tools for predicting and estimating effort in software development, were used. Objective: This paper aims to determine the convergence rate of each of the proposed ANNs, when obtaining the minimum relative error, first depending on the cost effect function, then on the nature of the data on which the training, testing, and validation is performed. Method: Magnitude relative error (MRE) is calculated based on Taguchi's orthogonal plans for each of these four proposed ANN architectures. The fuzzification method, five different datasets, the clustering method for input values of each dataset, and prediction were used to achieve the best model for estimation. Results: Based on performed parts of the experiment, it can be concluded that the convergence rate of each proposed architecture depends on the cost effect function and the nature of projects in different datasets. By following the prediction throughout all experimental parts, it can be further confirmed that ANN-L36 gave the best results in this proposed approach. Conclusion: The main advantages of this model are as follows: the number of iterations is less than 10, shortened effort estimation time thanks to convergence rate, simple architecture of each proposed ANN, large coverage of different values of actual project efficiency, and minimal MMRE. This model can also serve as an idea for the construction of a tool that would be able to reliably, efficiently and accurately estimate the effort when developing various software projects.