Rules, Inferences and Robust Approximation at Work

by Antonin Dvorak, Vilem Novak, Viktor Pavliska

How can a computer be taught to act like an experienced human being in complex situations? What sort of human-readable information can be extracted from numerical databases? Can we obtain new robust methods for approximation of functions and for solving differential equations? In addition, can we apply them, for example in signal filtering, compression and fusion of pictures, or the determination of ancient sea levels, when only very imprecise data are available? Soft computing methods are able to provide all of these, and even more.

Soft computing is a scientific discipline in which methods are developed that work effectively in presence of indeterminacy (ie imprecision and uncertainty), and provide practically optimal and inexpensive solutions in situations where only rough, imprecise information (very often expressed in natural language) is available.

Soft computing has been studied at the Institute for Research and Applications of Fuzzy Modelling (IRAFM) at the University of Ostrava in the Czech Republic for several years. In particular, two concepts have been investigated both theoretically and experimentally: fuzzy IF-THEN rules and fuzzy approximation. Recall that the former take a form such as "IF salary is more or less small AND quality of house is medium THEN mortgage coefficient is rather small".

Sets of fuzzy IF-THEN rules represent linguistic descriptions of control, decisions and other complex situations. We model these rules using formal fuzzy logic, with a strong emphasis on proper linguistic treatment of the expressions contained within them. This is accomplished by means of:

• careful study of evaluating linguistic expressions (eg 'small, more or less high, approximately 26, roughly medium', etc). Such expressions are indispensable in human reasoning
• interpreting fuzzy IF-THEN rules as linguistically expressed logical implications (the theoretical framework is higher-order fuzzy logic)
• using a special inference method called Perception-based logical deduction.

The methodology enables us to communicate with the computer in (restricted) natural language, without needing to penetrate into the fuzzy logic machinery. The computer acts (performs inferences) similarly to a human such that it resembles a specific 'human partner'. We can also model sophisticated human reasoning, such as that accomplished in detective stories or complex decision-making.

Linguistic descriptions can be obtained from experts, or by learning from data, or by combination of both. For example, linguistic knowledge (in a human-friendly form) can be extracted from databases for complex queries containing vague notions. Another possibility is to build a linguistic description from a successful course of control, eg of a technological process, mobile robot etc. Using our methods, we can also search the so-called linguistic associations in numerical data, eg "a significantly small crime rate AND a large proportion of residential land IMPLY more or less medium housing value". Such associations characterize relations in the data in a way that is closer to the way of thinking of experts from various fields.

Fuzzy approximation is a class of methods for the approximation of classical functions using techniques of soft computing. We have elaborated approximation methods using relational interpretation of fuzzy IF-THEN rules and developed a new method called the fuzzy (F-)transform. This is a powerful method for approximating functions, which has a wide variety of applications, eg in signal processing, approximate solutions of differential equations (ordinary as well as partial), or in methods for the compression and/or fusion of pictures. Our methods are very robust, that is, they have a low sensitivity to changes in the input data (eg signal filtering depends very little on sampling).

Figure 1: Simulink interface of LFLC - simulation of control of simple dynamic system.

Figure 2: Demonstration of filtering abilities of F-transform.

Our software system LFLC (Linguistic Fuzzy Logic Controller) deals with linguistic descriptions and enables fuzzy approximation; an interface to MATLAB/Simulink is also available (see Figure 1). A large-scale application of our methods can be found in Kovohute Bridlicna, in the Czech Republic, where LFLC controls five massive aluminium furnaces.

IRAFM is a partner of the Research Centre DAR (Data/Algorithms/Decision Making), headed by the Institute of Information Theory and Automation of the Czech Academy of Sciences (an ERCIM member). Our goals in DAR include fuzzy modelling of complex processes (where linguistic descriptions play a key role) and a combination of stochastic and fuzzy models.

Link:
http://irafm.osu.cz/irafm

Please contact:
Antonin Dvorak, University of Ostrava, Czech Republic
Tel: +420 597 460 218
E-mail: antonin.dvorakosu.cz