Abstract: To do modeling of a inference system is necessary to analyze the properties of input-output of inference systems by means of the partition of entire input spaces and the reasoning methods and modeling presents the premise part identification and the consequent part identification. In this study, identification in the premise part separates input space by using Min-Max method and HCM clustering algorithm constructing input output data into the hard clusters and the consequent part is presented by a constant or polynomial functions in the form of simplified inference and quadratic inference and the identification of coefficients expresses the standard least square method. Membership function of the first half is separating input space into relation space partition and respective space partition by using Gaussian function and by using gas furnace process data which is widely used in intelligence science, we evaluate the performance. The generation of inference rules has the problem that the number of inference rules exponentially increases but we divide the input space into the scatter form by using HCM clustering algorithm.