Adam Mrózek

Rough Sets in Computer Implementation of Rule-Based Control of Industrial Processes

We discuss the use of elements of rough set theory in computer implementation of rule-based control of industrial processes. The notions of expert’s inference model for industrial process control and of control protocol which registers the expert’s decisions are introduced. The process of extraction of decision rules contained in the control protocol based on the rough set theory formalism is presented. An example of the analysis of control protocol concerning the control process of a rotary clinker kiln is chosen as an illustration.

Rough sets in hybrid methods for pattern recognition

The article shows how rough sets can be applied to improve the classification ability of a hybrid pattern recognition system. The system presented here consists of a feature extractor based on a computer‐generated hologram (CGH) playing the role of a ring‐wedge detector. Features extracted by it are shift, rotation, and scale invariant. Although they can be optimized, no method has been proposed in the literature. This article presents an original method of optimizing the feature extraction abilities of a CGH. The method uses rough set theory (RST) to measure the amount of essential information contained in the feature vector. This measure is used to define an objective function in the optimization process. Since RST‐based factors are not differentiable, we use a nongradient approach for a search in the space of possible solutions. Finally, RST is used to determine decision rules for the classification of feature vectors. The alternative method of classification based on neural networks is also discussed. The whole method is illustrated by a system recognizing the class of speckle pattern images indicating the class of distortion of optical fibers. © 2001 John Wiley & Sons, Inc.

RULE‐BASED STABILIZATION OF THE INVERTED PENDULUM

The inverted pendulum poses serious problems for qualitative modeling methods, so it is a good benchmark to lest their performance. This paper shows how a new data analysis method known as rough set theory can be utilized to swing up and stabilize the pendulum. Our approach to this task consists of deriving control rules from the actions of a human operator stabilizing the pendulum and subsequently using them for automatic control. Rule derivation is based on the “learning from examples” principle and does not require knowledge of a quantitative model of the system.

A new method for discovering rules from examples in expert systems

Abstract The experts often cannot explain why they choose this or that decision in terms of formalized “if-then” rules; in these cases we have a set of examples of their real decisions, and it is necessary to reveal the rules from these examples. The existing methods of discovering rules from examples either demand that the set of examples be in some sense complete (and it is often not complete) or they are too complicated. We present a new algorithm which is always applicable. This algorithm is based on the formalization of rough set theory, a formalization which describes the case of incomplete information.

Rough Sets in Economic Applications

Making economic decisions is indeed a very interesting and perspective domain for many applications of methods and tools of computer science. However, economic decision problems are difficult to formalize. First of all it results from their complex character and great number of parameters describing their evolution, inexplicitness and incompleteness of available information as well as shortage of explicit criteria explaining economic decisions. Thus in economic decisions we often use intuition and knowledge which is accumulated in the process of creative generalization of practical experiments and observation results or empirical analysis. The same should be obviously considered during development of computer systems which support the process of making economic decisions.

Rough Sets in Industrial Applications

The design and implementation of industrial control systems often relies on quantitative models. At times, however, we encounter problems for which such models do not exist or are difficult and expensive to obtain. In such cases it is often possible to consult human experts to create qualitative models. This approach is the cornerstone of the application of fuzzy logic to the synthesis of control systems [3]. Another approach consists in observing human operators of plants and processes and discovering rules governing their actions. The behavior of operators can often be specified by decision tables, defined as sets of decision rules coupled with rule selection mechanisms. Rough set theory [10, 11] can be used to generate such tables from protocols of control, containing the decisions of human operators [8].

Knowledge Representation in Fuzzy and Rough Controllers

Alternative approaches to data processing, e.g., fuzzy set theory, rough set theory and neural networks, known collectively as ‘soft computing,’ have drawn significant interest from the scientific community. They have already found numerous applications to real-world problems and will certainly become even more important in the future. This paper concentrates on two important classes of soft computing methods, i.e., fuzzy sets and rough sets. In particular, knowledge acquisition and representation in fuzzy and rough controllers is discussed and compared. The paper is concluded with an illustrative example, showing the application of fuzzy and rough set theory to the control of the ‘inverted pendulum.’

Fiber optic sensor with a few-mode speckle pattern recognized by diffraction method

The construction of the fiber-optic sensor for the recognition of perturbations and results of its studies are presented. As a sensor head, the sample of few-mode optical fiber is used. Changes of intermodal interference condition, caused by external perturbation, have generated changes of output speckle pattern. This output has been concerned as an intensity image and diffraction method has been applied for its recognition. The image feature extraction has been achieved by applying a computer-generated hologram in the Fourier plane of an output image. A size of ring and wedge generated by this hologram has been optimized by using the rough set theory. Then, a artificial neural network has been used to recognize the external perturbation without a necessary of troublesome analysis of intermode interactions. An additional advantage of this solution is the possibility to train the network to eliminate slow environmental perturbations.

Rough Rules in Prolog

In this paper we present an approach to develop decision support systems. We focus on knowledge acquisition and processing with the use of rough set theory. The rule knowledge representation is also considered. We discuss the use of Prolog as a tool for knowledge representation and processing. Finally, the way of embedding Prolog code in procedural language programs is presented. Our work is illustrated with an exemplary system supporting credit decisions.

Optical fiber and genetically optimized computer-generated hologram force detection and classification

Quasi-monomode optical fiber sensors, used an input of systems for external force detection and classification, are widely described in references. Feature extractors in such systems are often based on computer generated holograms (CGH) and classifiers are usually built as artificial neural networks (ANN). The use of CGH instead of ring-wedge detector gives possibility of easy change of ring and wedge sizes. In this paper we present our method of CGH optimization. This method is based on evolutionary algorithms and elements algorithms and elements from rough set theory (RST). The results of classification of features obtained by applying optimized by our method CGH confirm that proposed approach can be successfully used for detection and classification of external force. All what is needed for this purpose is to pass coherent light through quasi-monomode optical fiber, and to place CGH in a focal plane of the lens. As CGH regions are the subject to be optimized to given application and therefore minimized in size, the resulting hybrid optic-digital system can be compact and relatively cheap. The experimental results for classification of generated by optimized CGH features confirmed the good overall quality of the proposed system.