This paper introduces a new learning algorithm for artificial neural networks, based on a fuzzy inference system ANBLIR.It is a computationally effective neuro-fuzzy system with parametrized fuzzy sets in the consequent parts of fuzzy if-thenrules, which uses a conjunctive as well as a logical interpretation of those rules. In the original approach, the estimationof unknown system parameters was made by means of a combination of both gradient and least-squares methods. Thenovelty of the learning algorithm consists in the application of a deterministic annealing optimization method. It leads to animprovement in the neuro-fuzzy modelling performance. To show the validity of the introduced method, two examples ofapplication concerning chaotic time series prediction and system identification problems are provided.