This paper proposes a new, improved COmmon Software Measurement International Consortium function point (COSMIC FP) method that uses Artificial Neural Network (ANN) architectures based on Taguchi's Orthogonal Array to estimate software development effort. The minimum magnitude relative error (MRE) to evaluate these architectures considering the cost effect function, the type of data used in the training, testing, and validation of the proposed models, was used. Applying the fuzzification and clustering method to obtain seven different datasets, we would like to achieve excellent reliability and accuracy of the obtained results. Besides examining the influence of four input values, we aim to reduce the risks of potential errors, increase the coverage of a wide range of different projects and increase the efficiency and success of completing many various software projects. The main contributions of our work are as follows: the influence of four input values of the COSMIC FP method on the change of mean (MRE), development of two simple ANN architectures, the attainment of a small number of performed iterations in software effort estimation (less than 7), reduced software effort estimation time, the use of different values of the International Software Benchmarking Standards Group and other datasets used in the experiment.