Reasoning with uncertainty

Because the rules or procedures in expert systems are heuristic they are often not well-defined in a logical sense. Nevertheless, they are used to draw conclusions. A conclusion can be uncertain because the truth of the rules deriving it cannot be established with 100% certainty or because the facts or evidence on which the rule is based are uncertain. Some measure of reliability of the obtained conclusions is therefore useful. There are different approaches used in expert systems to model uncertainty. They can be divided into methods that are based on 

Bayesian probability theory and methods that are based on fuzzy-set theory. The principles of both theories are explained in Chapter 16 and Chapter 19, respectively. Both approaches have advantages and disadvantages for the use in expert systems and it must be emphasized that none of the methods, developed up to now are satisfactory [7,11]. 

All these methods pretend to represent the intuitive way an expert deals with uncertainty. Whether this is true remains an open question. No method has yet been evaluated thoroughly. Modelling uncertainty to obtain a reasonable reliability measure for the conclusions remains one of the major unsolved issues in expert system technology. Therefore, it is important that in the expert system a mechanism is provided to define its boundaries, within which it is reasonably safe to accept the conclusions of the expert system. 

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Fuzzy logic is often referred to as a way of "reasoning with uncertainty." It provides a well-defined mechanism to deal with uncertain and incompletely defined data, so that one can make precise deductions from imprecise data. The incorporation of fuzzy ideas into expert systems allows the development of software that can reason in roughly the same way that people think when confronted with information that is ragged around the edges. Fuzzy logic is also convenient in that it can operate on not just imprecise data, but inaccurate data, or data about which we have doubts. It does not require that some underlying mathematical model be constructed before we start to assess the data. 

Panel on Reasoning with Uncertainty for Expert Systems, International Joint Conference on Artificial Intelligence, Los Angeles, California, 1985. 

Vol. 1093 L. Dorst, M. van Lambalgen, F. Voorbraak (Eds.), Reasoning with Uncertainty in Robotics. Proceedings, 1995. VIII, 387 pages. 1996. (Subseries LNAI). 

Fenton N E, Krause P and Neil M (2001a). Probabilistic Modelling for Software Quality Control. Sixth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty September 19-21, Toulouse, France, 2001. 

Some types of knowledge-based systems may make judgments based on data that contain uncertainty we shall learn more of this in the next chapter when we encounter fuzzy systems. Even when the information that the system reasons with is unambiguous, the system s conclusions may come as a surprise to a nonexpert. If the user doubts whether the ES has reasoned correctly, it is natural for them to seek reassurance that the line of reasoning used is robust, so the ES must be able to do more than merely provide advice, it should be able to explain how it has reached a particular conclusion. 

Shortliffe s proposal. In addition, we will experiment with a simplified, domain restricted form of explicit reasoning about uncertainty. 

The uncertainty in the estimate of (the value of y, at x = 0) is relatively large (s = j x29.48). Figure 8.7 suggests that this is reasonable - any uncertainty in the response will cause the parabolic curve to wiggle , and this wiggle will have a rather severe effect on the intersection of the parabola with the response axis. 

An important measurement is an accurate determination of the y-ray yield threshold for exciting a particular level. Thresholds can be determined with uncertainties of only a few keV, when necessary to guarantee certain placement of a y-ray in a level scheme. Usually, thresholds determined to within 30 to 50 keV are sufficient for this purpose, even in fairly heavy nuclei. The reason for this is that, typically, excited levels will have one or more decays to low-lying levels which are spaced 50 keV or more apart, even in heavy deformed nuclei. 

Why do people pad budgets with budgetary slack There are three primary reasons. First, people often perceive that their performance will look better in their superiors eyes if they can beat the budget. Second, budgetary slack often is used to cope with uncertainty. 

However, the paradigm and formalism of decision analysis doesn t capture everything that is important in real policy analysis environments. Tliere are a number of other reasons vdiy it may be important to characterize and deal with uncertainty in analysis even when the EVIU in a decision analytic context is zero or very small. Here are several ... 

Is my uncertainty reasonable What uncertainty is acceptable There is no simple answer to this It all depends on what the answer will be used for and how much time you have. Essentially you must make a measurement with sufficient accuracy to allow appropriate decisions to be made. This is known as fit for purpose. (Section 1.10)... 

The preceding uncertainty equations presume that all pairs of input estimates are uncorrelated, which may or may not be true. One of the most common examples of correlated input estimates in radioanalytical chemistry occurs when the chemical yield Y is calculated from an equation involving the counting efficiency e. This happens in measurements by alpha-particle spectrometry with an isotopic tracer. In this case, the uncertainty equation can be simplified by treating the product e x T as a single variable. What happens in effect is that the efficiency cancels out of the activity equation and for this reason its uncertainty can be considered to be zero ... 

Equation 22.17 can now be solved to give the pressure as a function of time for the entire three-dimensional interior of the reactor, provided that pressure values at two points in time are known. For a reactor sketched in Figure 22.13, the calculated pressure distribution in a plane at a height of 0.02 m above the transducer is shown in Figure 22.14 (Dahnke et al., 199b). The complex nature of the pressure distribution is easy to see. The conversion in any reactor will also be a function of space and time, and there is no method known yet for calculating it. A reasonable method would be to calculate the volume fraction of the bubbles and relate it to conversion empirically. Even this method is beset with uncertainties since only a part of the cavitational bubbles leads to sonochemical events. Much research needs to be done before a rational method of correlating conversion with cavitation can be established. 

Statistical Techniques associated with Exploratory Data Analysis. The overall KDD process also encompasses the task of Uncertainty Handling. Real-world data are often subject to uncertainty of various kinds, including missing values, and a whole range of Uncertainty Methods may be used in different approaches to reasoning under uncertainty. 

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