Amjad AlSakarneh
Mathematics, fuzzy models, linguistic modelling, fuzzy statistics, data analysis
Fuzzy and intelligent modelling is one of the powerful features of the intelligent system that overcame classical modelling. In this paper, a methodology is proposed to develop the optimum fuzzy model of single input-single output data; the data could be a model of physical system or a statistical data. The methodology used was to develop two models. The first one is based on Mamdani as inference mechanism, with aggregation type AND and defuzzification method the centre of gravity (CoG). The second model is based on Takagi–Sugeno inference mechanism, the aggregation type and defuzzification method are AND and CoG, respectively. Presuming that each input crisp excites all input membership functions (MFs); the linguistic input–output MFs, IF-THEN rules, fuzzification and defuzzification are converted to a single highly non-linear equation. Afterwards, the least square method, which was implemented in Matlab, is used as an optimization technique to fit the data. Finally, the proposed algorithm is applied and tested on some non-linear functions.
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