How to select and how to rank projects: The Promethee method

In this paper, we present the Promethee methods, a new class of outranking methods in multicriteria analysis. Their main features are simplicity, clearness and stability. The notion of generalized criterion is used to construct a valued outranking relation. All the parameters to be defined have an economic signification, so that the decision maker can easily fix them. Two ways of treatment are proposed: It is possible to obtain either a partial preorder (Promethee I) or a complete one (Promethee II), both on a finite set of feasible actions. A comparison is made with the Electre III method. The stability of the results given by the two methods is analysed. Numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed.     

On deciding how to decide: Designing participatory budget processes

Participatory budgets are becoming increasingly popular in many municipalities all around the world. The underlying idea is to allow citizens to participate in the allocation of a municipal budget. Many advantages have been suggested for such experiences, including legitimization and more informed and transparent decisions. There are many conceivable variants of such processes. However, in most cases both its design and implementation are carried out in an informal way. In this paper we propose a methodology to design a participatory budget process based on a multicriteria decision making model.     

To be or to become: how dynamic geometry changes discourse

In this article, we investigate the impact of the introduction of a dynamic geometry environment on mathematical thinking by identifying changes in discourse engendered by its introduction in a high school geometry class. Our focus is on the teacher, and we find significant differences between static and dynamic geometry in terms of the ways in which the teacher talks about geometric objects, makes use of visual artifacts and models geometric reasoning. Even though these changes have major implications for the geometry being studied, they are made only very implicitly in the classroom.     

Managerial influence on attitude formation in organizations: how to manage emergence

The emergence of a shared attitude in organizations can be regarded as a self-organizing complex process in which a majority attitude emerges from the ensemble of interactions among individuals. Almost by definition, emerging processes seem beyond the control of management, which is in conflict with the task of management to steer an organization. By modeling the emergence of a shared attitude in organizations, we were able to demonstrate that management had a distinct influence on this process. Furthermore, the first round of interactions was decisive for the outcome. The key to influencing the emergence of a shared attitude is to reduce resistance against the preferred attitude. High levels of group conformity inhibited conversion to the preferred attitude. Although the emergence of a shared attitude can be influenced by management, there remains an intrinsic uncertainty in the outcomes of attitude development processes.     

Dynamic repositioning strategy in a bike-sharing system; how to prioritize and how to rebalance a bike station

Bike-sharing systems are becoming increasingly popular in large cities. The natural imbalance and the stochasticity of bike’s arrivals and departures lead operators to develop redistribution strategies in order to ensure a sufficiently high quality of service for users. Using a Markov decision process approach, we develop an implementable decision-support tool which may help the operator to decide at any point of time (i) which station should be prioritized, and (ii) which number of bikes should be added or removed at each station. Our objective is to minimize the rate of arrival of unsatisfied users who find their station empty or full. The existence of an optimal inventory level at each station is proven. It may vary over time but does not depend on the capacity of the truck which operates the repositioning. Next, we compute the relative value function of the system, together with the average cost and the optimal state. These results are used to derive a policy for station’s prioritization using a one-step policy improvement method. We evaluate our policy in comparison with the optimal one and with other intuitive ones in an extended version of our model. From our numerical experiments, we show that only a little intervention of the operator can significantly enhance the quality of service, and that the rule of thumb for bike repositioning is to prioritize the closer, the more active, the closer to be full or empty, and the more imbalanced stations if no reversing in the imbalance is anticipated.     

Covariant quantum instruments

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.     

Computer type instruments

In the history of the art of measurement, computer type instruments have been in existence for a very short time. They can still be considered by-products of the computer technology, but there is no doubt that computer type instruments will in a future have the same importance for the human welfare and the evolution of sciences as electronic computers have to-day. In this article two examples are described, related to paper industry and nuclear physics research.     

Gluing semigroups: when and how

Semigroup Forum - Given two semigroups $$\langle A\rangle$$ and $$\langle B\rangle$$ in $${\mathbb {N}}^n$$ , we wonder when they can be glued, i.e., when there exists a semigroup $$\langle...     

Random A-permutations: Convergence to a Poisson process

Suppose that S _n is the permutation group of degree n, A is a subset of the set of natural numbers ?, and T _n(A) is the set of all permutations from S _n whose cycle lengths belong to the set A. Permutations from T _n are usually called A-permutations. We consider a wide class of sets A of positive asymptotic density. Suppose that ζ _mn is the number of cycles of length m of a random permutation uniformly distributed on T _n. It is shown in this paper that the finite-dimensional distributions of the random process {tz _mn, m ε A} weakly converge as n → ∞ to the finite-dimensional distributions of a Poisson process on A.     

Matrix monotonicity and self-concordance: how to handle quantum entropy in optimization problems

Let g be a continuously differentiable function whose derivative is matrix monotone on the positive semi-axis. Such a function induces a function \(\varphi (x)=\mathrm{tr}\, \big (g(x)\big )\) on the cone of squares of an arbitrary Euclidean Jordan algebra. We show that \(\varphi (x) - \ln \det (x)\) is a self-concordant function on the interior of the cone. We also show that \( -\ln (t-\varphi (x))-\ln \det (x)\) is \((r+1)\)-self-concordant barrier on the epigraph of \(\varphi ,\) where r is the rank of the Jordan algebra. The case \(\phi (x)=\mathrm{tr(x\ln x)}\) is discussed in detail.