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
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
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
On the Structure of Some Families of Fuzzy Measures
IEEE Transactions on Fuzzy Systems
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In this paper we deal with the problem of studying the structure of the polytope of fuzzy measures for finite referential sets. We prove that the diameter of the polytope of fuzzy measures is 3 for referentials of 3 elements or more. We also show that the polytope is combinatorial, whence we deduce that the adjacency graph of fuzzy measures is Hamilton connected if the cardinality of the referential set is not 2. We also give some results about the facets and edges of this polytope. Finally, we treat the corresponding results for the polytope given by the convex hull of monotone boolean functions.