Is there any exact number of variables that can be handled properly (rule base and membership functions) as input variables to a fuzzy inference system. I have been able to handle maximum 4 input variables manually. If possible provide the journal or article where it has been stated so.
There is no limits of variables! However, the more variables you have, the more difficulty will be the analysis and the visualization in the graphics! Perhaps, you can decouple a system in subsystems and then it may be easier to analyze a larger number of variables. Kind Regards, Farley.
Increasing the number of variables and the size of training data may cause problems so-called “fuzzy rule explosion” , however, there are many approach to deal with this problem.
1- try to reduce the number of variables using methods such as PCA (Principal Components Analysis).
2- try to cluster dataset in order to reduce the number of fuzzy rules and corresponding tunable parameter.
3- Employing hierarchical fuzzy systems (HFS) structure.
However, for your case with 4 variables is not too much !
If you have problem to define the fuzzy structure, it is suggested to employ fuzzy C-mean clustering.
See this book:
Jyh-Shing Roger Jang, Chuen-Tsai Sun, Eiji Mizutani , Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall; 1 edition ,1997,
Also:
1) Zajaczkowski, J., and Verma, B. (2012). Selection and impact of different topologies in multi-layered hierarchical fuzzy systems, Appl Intell, 36, 564-584.
2) Campello, R.J.G.B., Von Zuben, F.J., Amaral, W.C., Meleiro, L.A.C., and Maciel Filho, R. (2003). Hierarchical fuzzy models within the framework of orthonormal basis functions and their application to bioprocess control, Chem Eng Sci, 58, 4259- 4270.
3) Hines, J.W., and Wrest, D.J. (1997). Signal validation using an adaptive neural fuzzy inference system, Nucl Technol, 119, 181-193.
4) Chaibakhsh, A. (2012). Modelling and long-term simulation of a heat recovery steam generator, Math Comp Model Dyn, 19, 91-114.
5) Babŭka, R., and Verbruggen, H. (2003). Neuro-fuzzy methods for nonlinear system identification, Annu Rev Control, 27, 73-85.
Formally speaking, there is no limit on a number of variables. Although increasing number of variables in a fuzzy model we increase the complexity exponentially. In my approach i separate variables as a complex number according to their role in a model. This approach gives an opportunity to balance a fuzzy model. Details are in the publication
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