Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.

Solderjet bumping technique used to manufacture a compact and robust green solid-state laser

Solder-joining using metallic solder alloys is an alternative to adhesive bonding. Laser-based soldering processes are especially well suited for the joining of optical components made of fragile and brittle materials such as glasses, ceramics and optical crystals due to a localized and minimized input of thermal energy. The Solderjet Bumping technique is used to assemble a miniaturized laser resonator in order to obtain higher robustness, wider thermal conductivity performance, higher vacuum and radiation compatibility, and better heat and long term stability compared with identical glued devices. The resulting assembled compact and robust green diode-pumped solid-state laser is part of the future Raman Laser Spectrometer designed for the Exomars European Space Agency (ESA) space mission 2018.