Characterizing isometries on the order polytope with an application to the theory of fuzzy measures. (English) Zbl 1227.05035
Summary: We study the group of isometries over the order polytope of a poset. We provide a result that characterizes any isometry based on the order structure in the original poset. From this result we provide upper bounds for the number of isometries over the order polytope in terms of its number of connected components. Finally, as an example for an application, we recover the set of isometries for the polytope of fuzzy measures and the polytope of \(p\)-symmetric measures when the indifference partition is fixed.
MSC:
| 05A15 | Exact enumeration problems, generating functions |
| 06A07 | Combinatorics of partially ordered sets |
| 28E10 | Fuzzy measure theory |
| 52B20 | Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) |
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