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The paper presents a new system identification methodology for industrial systems. Using the original Mamdani fuzzy rule based system (FRBS), an adaptive Mamdani fuzzy modeling (AMFM) is introduced in this paper. It differs from the original Mamdani FRBS in that it applies different membership functions and a denazification mechanism that is `differentiable' with respect to the membership function parameters. The proposed system also includes a back error propagation (BEP) algorithm that is used to refine the fuzzy model. The efficacy of the proposed AMFM approach is demonstrated through the experimental trails from a compressor in an industrial gas turbine system.