Linguistic approximation of nonconvex membership functions using “...Except...” or “...Or...”

The authors´ recent work, “Decision risk minimization by computation semiotics” produced nonconvex membership functions describing the risk profiles of alternative strategies. Arguably, linguistic approximation of these fuzzy membership functions facilitates the choice decision by a human agent. As is often the case, membership functions are not convex when they result from aggregated or computed from real-world information. Two approaches to linguistic approximation are compared in this research: a) first finding a convex hull for a membership function and then excepting the concave (nonconvex) portion, and b) partitioning the membership function into convex portions and connecting the separately linguistically approximated terms with “... Or...”