Inclines and incline matrices: a survey

Inclines are additively idempotent semirings in which products are less than or equal to either factor. Thus they generalize Boolean and fuzzy algebra. We outline results obtained in a book with Cao [Cao, Kim, Roush, Incline Algebra and Applications, John Wiley & Sons, New York, 1984] on algebraic structure of inclines themselves, matrices over inclines, topological and convergence results, and some applications. This survey paper represents our talk at the 10th annual ILAS conference at Auburn University, June 2002.