How to tell when a product of two partially ordered spaces has a certain property: General results with application to fuzzy logic

In this paper, we describe how checking whether a given property F is true for a product A₁ × A₂ of partially ordered spaces can be reduced to checking several related properties of the original spaces A_i. This result in useful in fuzzy logic, where, to compare our degree of confidence in several statements, we often need to combine relative confidence comparison results provided by different experts. For example, Cartesian product corresponds to the cautious approach, when our confidence in S^´ is higher than confidence in S if and only if all the experts are more confident in S^´ than in S. Alternatively, if we have an absolute confidence in the first expert and we use the opinion of the second expert only if the first expert cannot decide, we get a lexicographic product.