12.4 Review/Preview

In this chapter we have presented the idea of using fuzzy mathematics for developing computer models. Developing a fuzzy model is closely related to developing a fuzzy controller; they both involve the construction of a surface in hyperspace. Thus, the step-by-step procedure for developing a fuzzy controller presented in Chapter 2 was modified to produce a step-by-step procedure for developing a fuzzy model. This procedure was used to develop computer models of two industrial systems: a grinding circuit and a flotation system.

As with fuzzy controllers, one of the delicate issues associated with fuzzy model development is the selection of rules and the tuning of membership functions. If we have done a reasonable job of presenting the material in this book to the current point, the reader should need no encouragement to select a genetic algorithm for this task. And, a genetic algorithm was used in this chapter to tune both the grinding and flotation models.

Fuzzy mathematics offers another approach to developing computer models. This approach has some nice features. The next section of the book provides detailed descriptions in which computer models have been incorporated into controllers to supply the adaptive capabilities needed to effectively control complex industrial systems.

References

Karr, C. L. (1993a). Strategy for adaptive process control for a column flotation unit: Proceedings of the Fifth Workshop on Neural Networks, SPIE 2204, 95–100.

Karr, C. L. (1993b). Optimization of a computer model of a grinding process using genetic algorithms: In H. El-Shall, B. Moudgil, and R. Weigel, Beneficiation of Phosphate: Theory and Practice. Littleton, CO: Society for Mining, Metallurgy, and Exploration, 339–345.

Karr, C. L., Yeager, D., and Stanley, D. A. (1994). Tuning empirical computer models using genetic algorithms: Proceedings of the Society of Computer Simulation Summer Conference, 236-241.

Kelly, E. G., and Spottiswood, D. J. (1982). Introduction to mineral processing, New York, NY: John Wiley & Sons.

Wasserman, P. D. (1989). Neural computing, New York, NY: Van Nostrand Reinhold.