How to Tell When a Product of Two Partially Ordered Spaces Has a Certain Property?

Publication Date


Document Type

Conference Proceeding


2011 Annual Meeting of the North American Fuzzy Information Processing Society
DOI: 10.1109/NAFIPS.2011.5752044


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 Ai. 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.