Fuzzy rules

All the three techniques mentioned above may make use of fuzzy sets and fuzzy logic (for fuzzy classification, fuzzy rules or fuzzy matching) but this does not effect the discussion of the applicability to NDT problems in the next section. 

Fuzzy Logic Control The apphcation of fuzzy logic to process control requires the concepts of Fuzzy rules and fuzzy inference. A fuzzy rule, also known as a fuzzy IF-THEN statement, has the form ... 

Chen et al. [24] provide a good review of Al techniques used for modeling environmental systems. Pongracz et al. [25] presents the application of a fuzzy-rule based modeling technique to predict regional drought. Artificial neural networks model have been applied for mountainous water-resources management in Cyprus [26] and to forecast raw-water quality parameters for the North Saskatchewan River [27]. 

Pongracz R, Bogardi I, Duckstein L (1999) Application of fuzzy rule-based modelling technique to regional drought. J Hydrol 224 100-114... 

Harrington, P. B. Fuzzy Rule-building Expert Systems Minimal Neural Networks. J. Chemometrics 1991, 5, 467 186. 

Within a fuzzy system, an inference engine works with fuzzy rules it takes input, part of which may be fuzzy, and generates output, some or all of which may be fuzzy. Although the role of a fuzzy system is to deal with uncertain data, the input is itself not necessarily fuzzy. For example, the data fed into the system might consist of the pH of a solution or the molecular weight of a compound, both of which can be specified with minimal uncertainty. In addition, the output that the system is required to produce is of more value if it is provided in a form that is crisp "Set the thermostat to 78°C" is more helpful to a scientist than "raise the temperature of the oven." Consequently, the fuzzy core of the inference engine is bracketed by one step that can turn crisp data into fuzzy data, and another that does the reverse. 

We could express the activity of fumerase as a function of pH in the fuzzy rules ... 

In order to reason using fuzzy data, a way must be found to express rules so that the degree of certainty in knowledge can be taken into account and a level of certainty can be ascribed to conclusions. This is done through fuzzy rules. A fuzzy rule has the form ... 

The relationships described form the concept (Fig. 5.68) of the FUZZY RULE SET. The membership-functions of the linguistic variables are derived from the experiments that have already been mentioned however, the plausibilities of the RULE SET have not been touched on so far. 

Fusion power, noble gases and, 17 375 Fusion process, 9 278 10 361-364, 365 Fusion reactors, vanadium in, 25 526 FutureGen Program (Department of Energy), 13 845 Fuzzy logic control, 20 698-699 Fuzzy rules, 20 699 F values, 13 252... 

In fuzzy logic, the use of fuzzy if-then rules is governed by the calculus of fuzzy rules, CFR. A major part of CFR is the Fuzzy Dependency and Command Language, or FDCL for short. Basically, FDCL is a fuzzy programming language that provides a powerful tool for the representation and manipulation of imprecise or ill-defined dependencies. Two issues play pivotal roles in FDCL. The first is interpolation, and the second relates to the induction of rules from observations. 

Fig. 8 Fuzzy rules for controlling a fan heater based on fuzzy concepts of room temperature (COLD, COOL, WARM, HOT).

Adriaenssens, V., Baets, B.D., Goethals, P.LM. and Pauw, N.D. (2004) Fuzzy rule-based models for decision support in ecosystem management, Sci. Total Environ., 319, pp. 1-12. 

Fuzzy inference systems are also known as fuzzy associative memories, fuzzy models, fuzzy-rule-based systems, or fuzzy controllers. 

Here, the premise is described by a membership function for the linguistic variable high and the function for the detection limit is the sum of the blank signal, y, and three times the standard deviation of the blank signal, Sg, (cf. Eq. (4.3)). Optimization of the parameters in the premise part of the rules is adaptively done by combining the fuzzy rule-based system with a neural network. Consider an adaptive neuro-fuzzy system with two inputs, and... 

Compare symbolic knowledge processing in case of crisp and fuzzy-rule-based systems. 

Recovery Computer systems may apply techniques of artificial intelligence (Al) (e.g., fuzzy rules, knowledge-based logic, neural networks) to improve the quality of activities. For example, a robot system may be recovered automatically from error conditions through decisions made by AI programs. 

Figure 6 shows a structure of applying fuzzy logic in control. First, two types of inputs must be obtained numerical inputs and human knowledge or rule extraction from data (i.e., fuzzy rules). Then the numerical inputs must be fuzzified into fuzzy numbers. The fuzzy rules consist of the fuzzy membership functions (knowledge model) or so-called fuzzy associative memories (FAMs). Then the... 

Chang, T. (1996), A Fuzzy Rule-Based Methodology for Dynamic Kanban Control in a Generic Kanban System, Ph.D. dissertation, Purdue University, West Lafayette, IN. 

Chang, T., and Yih, Y. (1998), A Fuzzy Rule-Based Approach for Dynamic control of kanbans in a generic kanban system, International Journal of Production Research, Vol. 36, No. 8, pp. 2247-2257. 

There are several kinds of fuzzy rules used to construct fuzzy models. These fuzzy rules can be classified into the following three types according to their consequent form [107] ... 

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