data envelopment analysis (dea) is an eciency measurement tool for evaluation of similar decision making units (dmus). in dea, weights are assigned to inputs and outputs and the absolute eciency score is obtained by the ratio of weighted sum of outputs to weighted sum of inputs. in traditional dea models, this measure is also equivalent with relative eciency score which evaluates dmus in com...

We discuss the relationship between matroid rank functions and a concept of discrete concavity called M-concavity. It is known that a matroid rank function and its weighted version called a weighted rank function are M-concave functions, while the (weighted) sum of matroid rank functions is not M-concave in general. We present a sufficient condition for a weighted sum of matroid rank functions ...

Considering a vector optimization problem to which properly efficient solutions are defined by using convex cone-monotone scalarization functions, we attach to it, by means of perturbation theory, new vector duals. When the primal problem, the scalarization function and the perturbation function are particularized, different dual vector problems are obtained, some of them already known in the l...

A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the “yea” voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be integers. In [Freixas and Molinero(2009)] the authors have classified all weighted voting games without ...

Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...

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