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Adaptive neuro-fuzzy inference system (ANFIS) is efficient estimation model not only among neuro-fuzzy systems but also various other machine learning techniques. Despite acceptance among researchers, ANFIS suffers from limitations that halt applications in problems with large inputs; such as, curse of dimensionality and computational expense. Various approaches have been proposed in literature to overcome such shortcomings, however, there exists a considerable room of improvement. This paper reports approaches from literature that reduce computational complexity by architectural modifications as well as efficient training procedures. Moreover, as potential future directions, this paper also proposes conceptual solutions to the limitations highlighted.