How to score alternatives when criteria are scored on an ordinal scale

International audienceWe address in this paper the problem of scoring alternatives when they are evaluated with respect to several criteria on a finite ordinal scale $E$. We show that in general, the ordinal scale $E$ has to be refined or shrunk in order to be able to represent the preference of the decision maker by an aggregation operator belonging to the family of mean operators. The paper recalls previous theoretical results of the author giving necessary and sufficient conditions for a representation of preferences, and then focusses on describing practical algorithms and examples

Enumeration of Mycobacterium avium subsp. paratuberculosis by quantitative real-time PCR, culture on solid media and optical densitometry

<p>Abstract</p> <p>Background</p> <p>Different approaches are used for determining the number of <it>Mycobacterium avium </it>subsp. <it>paratuberculosis </it>(MAP) cells in a suspension. The majority of them are based upon culture (determination of CFU) or visual/instrumental direct counting of MAP cells. In this study, we have compared the culture method with a previously published F57 based quantitative real-time PCR (F57qPCR) method, to determine their relative abilities to count the number of three different MAP isolates in suspensions with the same optical densities (OD). McFarland turbidity standards were also compared with F57qPCR and culture, due to its frequent inclusion and use in MAP studies.</p> <p>Findings</p> <p>The numbers of MAP in two-fold serial dilutions of isolates with respective OD measurements were determined by F57qPCR and culture. It was found that culture provided lower MAP CFU counts by approximately two log₁₀, compared to F57qPCR. The McFarland standards (as defined for <it>E. coli</it>) showed an almost perfect fit with the enumeration of MAP performed by F57qPCR.</p> <p>Conclusions</p> <p>It is recommended to use culture and/or qPCR estimations of MAP numbers in experiments where all subsequent counts are performed using the same method. It is certainly not recommended the use of culture as the standard for qPCR experiments and <it>vice versa</it>.</p

On the mathematical foundations of MACBETH

MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is a multicriteria decision analysis approach that requires only qualitative judgements about differences of value to help an individual or a group quantify the relative attractiveness of options. We present an up-to-date survey of the mathematical foundations of MACBETH. Reference is also made to real-world applications and an extensive bibliography, spanning back to the early 1990’s, is provided