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The main objective of this model is to focus on how to use the model of fuzzy system to solve fuzzy mathematics problems. Some mathematical models based on fuzzy set theory, fuzzy systems and neural network techniques seem very well suited for typical technical problems. We have proposed an extension model of a fuzzy system to N-dimension, using Mamdani's minimum implication, the minimum inference system, and the singleton fuzzifier with the center average defuzzifier. Here construct two different models namely a fuzzy inference system and an adaptive fuzzy system using neural network. We have extended the theorem for accuracy of the fuzzy system to Ndimensions, and provided a medical application of the fuzzy mathematics models. Since, liver is the largest internal member in the human body, so diagnosing liver disorder disease is a high interest to researchers of the fuzzy modeling and the fuzzy system. Therefore, the fuzzy mathematical models are applied on a real data to the Liver Disorder disease. Consequently, a comparison between three models: the FS with Mamdani model, ST model, and the ANFIS is made. Therefore, we have obtained the best result with the ANFIS. Finally, the programs of these models by using MATLAB created and performed.

Fuzzy mathematical models for the analysis of fuzzy systems with application to liver disorders