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To illustrate the implementation of hedges, consider again the set of tall people, and assume the membership function ntall characterizes the degree of membership of elements to the set tall. Our task is to create a new set, very. tall of people that are very tall. In this case, the hedge very can be implemented as the square function. That is, p.very_tall(x) = u t a l l (x) 2 - Hence, if Peter belongs to the set tall with certainty 0.9, then he also belongs to the set very -tall with certainty 0.81. This makes sense according to our natural understanding of the phrase very tall: Degree of membership to the set very-tall should be less than membership to the set tall. Alternatively, consider the set sort-of-tall to represent all people that are sort of tall, i.e. people that are shorter than tall. In this case, the hedge sort of can be implemented as the square root function, p- Sort-oj_tall (x} \/t*tall(%)- So, if Peter belongs to the set tall with degree 0.81, he belongs to the set sort-of-tall with degree 0.9. Different kinds of hedges can be defined, as listed below: Concentration hedges (e.g. very), where the membership values get relatively smaller. That is, the membership values get more concentrated around points with higher membership degrees. Concentration hedges can be defined, in general terms, as P , forp>l where A is the concentration of set A. Dilation hedges (e.g. somewhat, sort of, generally), where membership values increases. Dilation hedges are defined, in general, as HA>(x) = A(X)

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1 Many system administrators originate from scientific disciplines and are already well-versed in scientific methods, but this could change as the future washes over us... and it never hurts to be reminded of basic techniques.

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we are able to perform this extraction of the foundations some study, and if that knowledge empowers us with some increased understanding of the problem In science, knowledge advances by undertaking a series of studies, in order to either verify or falsify a hypothesis Sometimes these studies are theoretical, sometimes they are empirical, and frequently they are a mixture of the two The aim of a study is to contribute to a larger discussion, which will eventually lead to progress in the field A single piece of work is rarely, if ever, an end in itself Once a piece of work is published, it needs to be verified or shown to be false by others also Reproducibility is an important criterion for any result, otherwise it is worthless How we measure progress in a field is often a contentious issue, but it can involve several themes.

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Contrast intensification hedges (e.g. extremely), where memberships lower than I/ are diminished, but memberships larger than 1/2 are elevated. This hedge is defined as, P-IHA(X)P .-2P-l(l-uA(x))P which intensifies contrast. Vague hedges (e.g. seldom), are opposite to contrast intensification hedges, having membership values altered using

To test an idea it is often necessary to develop a suitable 'technology' for the investigation That technology might be mathematical, computational or mechanical It does not relate directly to the study itself, but it makes it possible for the study to take place In system administration, software tools form this technology For example, the author's management system cfengine [32] is a tool which was created to implement and refine a conceptual scheme, namely the immunity model of system maintenance [35] There is a distinction between the tool which makes the idea possible, and the idea itself Having produced the tool, it is still necessary to test whether or not the original idea was a good one, better or worse than other ideas, or simply unworkable in practice.

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Scientific progress is made with the assistance of a tool only if the results of previous work can be improved upon, or if an increased understanding of the problem can be achieved, perhaps leading to greater predictive power or a more efficient solution to the original problem All problems are pieces of a larger puzzle A complete scientific study begins with a motivation, followed by an appraisal of the problems, the construction of a theoretical model for understanding or solving the problems, and finally, an evaluation or verification of the approach used and the results obtained Recently, much discussion has been directed towards finding suitable methods for evaluating technological innovations in computer science, as well as to encouraging researchers to use them.

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Nowadays, many computing systems are of comparable complexity to phenomena found in the natural world, and our understanding of them is not always complete, in spite of the fact that they were designed to fulfil a specific task In short, technology might not be completely predictable, hence there is a need for experimental verification..

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