Mastering modern industrial processes requires the use of modern approaches in planning and optimization, and their implementation by efficient decision support systems. Recently, soft computing approaches based on fuzzy logic have been considered in the design of expert decision support systems.

This paper proposes a soft computing approach that takes into account fuzzy ontologies--namely, fuzzy relations--useful in various application domains described in terms of inputs and outputs. The authors explain their methodology for mastering the processes of paper machines. The main sections of the papermaking machines perform the main processes, including forming, pressing, drying, and calendaring. Using a decision system based on the knowledge of experienced engineers (experts) during the training of inexperienced operators helps the authors identify the optimum combination of productive factors that assure the best operation during the industrial process.

The mathematical model of the paper machine uses a finite set of factors, a set of characteristics, and a relation of factors and characteristics represented on a scale with two polarities describing the intensity of the factor positively or negatively affecting the characteristic. The authors use numbers from the interval [-1,1] to model the degree of intensity, and explain how to consider fuzzy numbers to extend the model to include imprecision aspects.

The underlying model involves fuzzy goal programming, in which fuzzy weights are associated with imprecisely specified goals. The optimal partitioning of factors and characteristics is obtained by solving a multiobjective optimization problem reduced, finally, to a linear optimization problem.

The paper concludes with possible improvements of the model, the model implementation in Excel, and a discussion of the management of paper machine processes.

The material is well organized in seven sections, with a clear and complete presentation of the proposed methodology, a list of suitable references, the general framework, and the case study on the paper machines. In my opinion, the presented approach can be used to optimize various processes described by soft (fuzzy type) relations between factors (as system inputs) and characteristics (as system outputs).