Industrial process optimization and decision-making are often in a fuzzy environment. Measurements from on-line sensors may be noisy and inaccurate. Complete and accurate data and models may not be available. Domain knowledge are sometimes represented in empirical equations and linguistic descriptions. For optimization in a fuzzy environment, most published work focuses on different forms of fuzzy linear programming (Zimmermann, 1992). We have, however, concentrated on the following aspects of the problem: (a) Linearity can not always be guaranteed in most industrial processes. To avoid distortion, non-linearity has been taken into consideration, (b) We distinguished two types of system constraints: equality relationships and inequality constraints. There is a distinct difference in fuzziness between them. Inequality constraints address imprecise and non-crisp boundaries, around which a slight violation would be tolerated. While fuzzy equations indicate fuzziness of poorly-understood relationships among process variables. In this paper, a fuzzy relational modeling approach is described, and the corresponding optimization methodology is developed. As a case study, we present how a fuzzy modeling and optimization approach can be used for a wood chip refining process and improvement of pulp quality.
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