Some methods for evaluating the optimality of elements in matroids with ill-known weights

In this paper a class of matroidal combinatorial optimization problems with imprecise weights of elements is considered. The imprecise weights are modeled by intervals and fuzzy intervals. The concepts of possible and necessary optimality under imprecision are recalled. Some efficient methods for evaluating the possible and necessary optimality of elements in the interval-valued problems are proposed. Some efficient algorithms for computing the exact degrees of possible and necessary optimality of elements in the fuzzy-valued problems are designed.

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