Applications of semirings in engineering and social sciences

There are presented two recent applications of special semirings. There is introduced an innovative concept in modelling operations of container quay cranes based on pseudo-analysis in the form of maxplus semiring. In social sciences the ordering on a semiring of monotone doubly stochastic matrices in Shorrocks' sense is investigated. It is identified a class of an equilibrium index of mobility that induces the full ordering in a semiring.