Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial functions, that is, functions built only on projections and minimum and maximum operations

Decomposition approaches to integration without a measure

Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of decompositions: sub-decomposition based integrals (in economics linked with optimization problems to maximize the possible profit) and super-decomposition based integrals (linked with costs minimization). We provide several examples (both theoretical and realistic) to stress that our approach generalizes that of Even and Lehrer [3] and also covers problems of linear programming and combinatorial optimization. Finally, we introduce some new types of integrals related to optimization tasks.Comment: 15 page

An Evaluation of Electrical Conductivity as a Practical Tool in Mastitis Detection at Andrews University Dairy

An infection in a cow\u27s udder, also known as mastitis, has been a persistent problem for the U.S. dairy community. Mastitis not only decreases milk production, but also shortens the productive life of dairy cattle and can be fatal if left untreated. Mastitis presents in both subclinical and clinical forms - clinical is easy to diagnose and treat, whereas subclinical cases are much harder to detect as they present no physical symptons, yet can still become clinical in time. At the Andrews University Dairy, part of the milking system includes electrical conductivity (EC) determination which measures the ionic composition of a cow\u27s milk as she is being milked. The milking management software (AFImilk) checks for increases in EC which may indicate subclinical mastitis; the system then alerts the milking parlor crew of elevated EC by a visual alarm and records the EC information on the cow\u27s individual record. However, the dairy management team has found that the current EC system offers too many unnecessary or false alarms to be a helpful diagnostic tool, and that it merely promotes the desensitizing of workers to the presence of alarms. The purpose of this study is to determine, based on dairy records, the practical ability of EC to determine if a cow has mastitis and needs antibiotic treatment. Data on EC was collected from 89 cows at the A.U. Dairy that had experienced at least one episode of clinical mastitis in their current lactation. This data was processed during particular statistical parameters to determine false alarm rate, and ultimately, the data was analyzed using Bayes\u27 Theorem to estimate the probability of a cow having mastitis given the presence of an alarm. Analyzing the accuracy and reliability of EC, this study has determined that the management\u27s distrust of EC is well-founded, not misguided. Our results showed that, due an an exceptionally high number of false alarms and unpredicted mastitis events, EC is not a practical took for detecting clinical mastitis in the milking parlor