Discrete & Computational Geometry
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
k-order additive discrete fuzzy measures and their representation
Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Generalizations of k-order additive discrete fuzzy measures
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
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Identification of fuzzy measures from sample data with genetic algorithms
Computers and Operations Research
On the polytope of non-additive measures
Fuzzy Sets and Systems
Characterizing isometries on the order polytope with an application to the theory of fuzzy measures
Information Sciences: an International Journal
Adjacency on the order polytope with applications to the theory of fuzzy measures
Fuzzy Sets and Systems
On the Structure of Some Families of Fuzzy Measures
IEEE Transactions on Fuzzy Systems
An algorithm for finding the vertices of the k-additive monotone core
Discrete Applied Mathematics
Robust optimization of the Choquet integral
Fuzzy Sets and Systems
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In this paper we present some results concerning the vertices of the set of fuzzy measures being at most k-additive. We provide an algorithm to compute them. We give some examples of the results obtained with this algorithm and give lower bounds on the number of vertices for the (n-1)-additive case, proving that it grows much faster than the number of vertices of the general fuzzy measures. The results in the paper suggest that the structure of k-additive measures might be more complex than expected from their definition and, in particular, that they are more complex than general fuzzy measures.