Discrete mathematics and its applications
Discrete mathematics and its applications
Sperner theory
k-order additive discrete fuzzy measures and their representation
Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Alternative representations of discrete fuzzy measures for decision making
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - Special issue on fuzzy measures and integrals in subjective evaluation
Algorithms counting monotone Boolean functions
Information Processing Letters
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Identification of fuzzy measures from sample data with genetic algorithms
Computers and Operations Research
On the Structure of Some Families of Fuzzy Measures
IEEE Transactions on Fuzzy Systems
The Polytope of Fuzzy Measures and Its Adjacency Graph
MDAI '08 Sabadell Proceedings of the 5th International Conference on Modeling Decisions for Artificial Intelligence
Adjacency on the order polytope with applications to the theory of fuzzy measures
Fuzzy Sets and Systems
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
Robust optimization of the Choquet integral
Fuzzy Sets and Systems
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In this paper we deal with the problem of studying the structure of the polytope of non-additive measures for finite referential sets. We give a necessary and sufficient condition for two extreme points of this polytope to be adjacent. We also show that it is possible to find out in polynomial time whether two vertices are adjacent. These results can be extended to the polytope given by the convex hull of monotone Boolean functions. We also give some results about the facets and edges of the polytope of non-additive measures; we prove that the diameter of the polytope is 3 for referentials of three elements or more. Finally, we show that the polytope is combinatorial and study the corresponding properties; more concretely, we show that the graph of non-additive measures is Hamilton connected if the cardinality of the referential set is not 2.