Fuzzy Rule Base Development

Fuzzy logic systems are knowledge-based or rule-based systems constructed from human knowledge in the form of fuzzy IF-THEN rales (Wang (1997)). An important contribution of fuzzy system theory is that it provides a systematic procedure for transforming a knowledge base into non-linear mapping. A fuzzy IF-THEN rule is an IF-THEN statement in which some words are characterised by continuous membership functions. 

IF-THEN rules have two parts an antecedent that is compared to the inputs and a consequent, which is the result/output. The input of the fuzzy rules base is the probability of occurrence. 

Using Equation (7.7), the membership function for the roles in the fuzzy rule base can be determined. The role base is then used in the FMEA to ascertain the priority for attention for each of the potential failure modes identified. 

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In conjunction with this fuzzy logic approach, a new chip-groove classification system was proposed, and the most significant geometric chip-groove parameters were identified from chip-groove profiles. A fuzzy rule-based system was developed based on the composite profile of the tool insert and its chip breakabiiity performance. 

The fuzzy rule base is developed in such a way so as to enable comparison with the traditional FMEA method. Hence, in fuzzy terms, the linguistic variables are determined to be the probability of occurrence, severity and detectability. Each of these variables can be described in linguistic terms as Remote, Low, Moderate, High and Very High. The interpretations of these linguistic terms have already been given in Table 7.4. 

Data of different units and uncertainties can be combined using IF... THEN... rules, based on expert knowledge. Recently, the application of the traceability concept on ecotoxicological studies has been described (Ahlf and Heise, 2007). A suggestion for an ecotoxicological classification system for sediments based on fuzzy sets and fuzzy expert systems is under development (see Chapter 6.2). 

The Advanced level includes sophisticated use of the large amount of measurement data fuzzy temperature control by concentrate feed, oxygen enrichment control by 02-feed and furnace top temperature control by water addition. Also, this level includes process monitoring by means of SOM, as well as an advisory system based on expert rules (under development). 

Fuzzy rules are generated based on available historical data, experience and complemented by expert knowledge. Where possible, logbooks are analysed for casualty and accident reports to develop the following rules ... 

Recently, a new approach called artificial neural networks (ANNs) is assisting engineers and scientists in their assessment of fuzzy information, Polymer scientists often face a situation where the rules governing the particular system are unknown or difficult to use. It also frequently becomes an arduous task to develop functional forms/empirical equations to describe a phenomena. Most of these complexities can be overcome with an ANN approach because of its ability to build an internal model based solely on the exposure in a training environment. Fault tolerance of ANNs has been found to be very advantageous in physical property predictions of polymers. This chapter presents a few such cases where the authors have successfully implemented an ANN-based approach for purpose of empirical modeling. These are not exhaustive by any means. 

A fuzzy system maps an input spaee to an output spaee by means linguistic rules, which is based on human reasoning. The linguistie representation presents an intuitive, natural description of a system allowing for relatively easy algorithm development compared to numerical systems. A fuzzy linguistic mle consists of an IF-THEN statement. A fuzzy mle is evaluated by means of fuzzy operators such as fuzzy AND , fuzzy OR etc. For example, in the case of two inputs (A and I2) and single output (O) fuzzy system, it can be expressed as shown below ... 

The term fuzzy logic in its true sense means imprecise logic. The concept behind it was developed in the 1960s by Lotfi A. Zadeh, University of Berkeley, California, USA (Zadeh, 1965). Fuzzy logic uses terms similar to human language to describe values of parameters and relations. These linguistic rules thus allow an easy transfer of human expert knowledge into a computer-based control system. 

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