Discrete & Computational Geometry
Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
Discrete mathematics and its applications
Discrete mathematics and its applications
Counting linear extensions is #P-complete
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Geometrical techniques for estimating numbers of linear extensions
European Journal of Combinatorics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Lectures on Discrete Geometry
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Identification of fuzzy measures from sample data with genetic algorithms
Computers and Operations Research
Algorithmic combinatorics based on slicing posets
Theoretical Computer Science
Exploiting the Lattice of Ideals Representation of a Poset
Fundamenta Informaticae
Incidence structures and Stone---Priestley duality
Annals of Mathematics and Artificial Intelligence
On the polytope of non-additive measures
Fuzzy Sets and Systems
Topics in Graph Theory: Graphs and Their Cartesian Product
Topics in Graph Theory: Graphs and Their Cartesian Product
On the Structure of Some Families of Fuzzy Measures
IEEE Transactions on Fuzzy Systems
An algorithm to generate the ideals of a partial order
Operations Research Letters
Characterizing isometries on the order polytope with an application to the theory of fuzzy measures
Information Sciences: an International Journal
On the structure of the k-additive fuzzy measures
Fuzzy Sets and Systems
Bases axioms and circuits axioms for fuzzifying matroids
Fuzzy Sets and Systems
On distorted probabilities and m-separable fuzzy measures
International Journal of Approximate Reasoning
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In this paper we study the adjacency structure of the order polytope of a poset. For a given poset, we determine whether two vertices in the corresponding order polytope are adjacent. This is done through filters in the original poset. We also prove that checking adjacency between two vertices can be done in quadratic time on the number of elements of the poset. As particular cases of order polytopes, we recover the adjacency structure of the set of fuzzy measures and obtain it for the set of p-symmetric measures for a given indifference partition; moreover, we show that the set of p-symmetric measures can be seen as the order polytope of a quotient set of the poset leading to fuzzy measures. From this property, we obtain the diameter of the set of p-symmetric measures. Finally, considering the set of p-symmetric measures as the order polytope of a direct product of chains, we obtain some other properties of these measures, as bounds on the volume and the number of vertices on certain cases.