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One of two aims of this paper is to briefly present two different types of neuro-fuzzy systems (neuro-fuzzy classifiers for the purposes of decision support, especially in medical domains) representing two main directions of synthesizing artificial neural networks and fuzzy logic within one, hybrid, neuro-fuzzy system. The second aim of this paper is to perform a comparative analysis of both proposed neuro-fuzzy systems and three other methodologies (rough-set inspired classifier, Quinlan's rule model and rule induction system CN2) applied to the common data set coming from the field of veterinary medicine and describing different aspects of selecting surgical and nonsurgical cases in the domain of equine colic. Three independent but cooperating subsystems predicting surgical or nonsurgical types of lesions as well as final outcomes of treatment have been designed and tested with the use of particular approaches.