Dealing with Uncertainties in MCDA

This chapter presents various approaches to incorporating formalmodelling of risks and uncertainties into multi-criteria decision analysis,in a theoretically valid but also operationally meaningful manner. Weconsider both internal uncertainties (in the formulation and modellingof the decision problem), and external uncertainties arising fromexogenous factors, but with greater attention paid to the latter. Aftera broad discussion on the meaning of uncertainty, we first reviewapproaches to sensitivity analysis, which is particularly, although notexclusively, relevant to internal uncertainties. We discuss the role,but also some limitations, of representing uncertainties in formalprobabilistic structures, linked also to concepts of expected (multiattribute) utility theory. Such probability/utility approaches may be usedin explicitly identifying a most preferred solution, or simply to eliminatecertain courses of action when stochastically dominated (in varioussenses) by others. In some contexts it may be useful to view minimizationof various risk measures as additional criteria in more standard MCDAmodels, and we comment on advantages and disadvantages of suchapproaches. Finally we discuss the integration of MCDA with scenarioplanning, in order to deal with deeper uncertainties (not easily if at allrepresentable by probability models), particularly in a strategic planningcontext. The emphasis throughout is on the practice of MCDA rather thanon esoteric theoretical results.<br/

The ‘Self-Regulated Learning Opportunities Questionnaire': a diagnostic instrument for teacher educators' professional development

Many recent studies have stressed the importance of students’ self-regulated learning (SRL) skills for successful learning. Although primary teacher educators are aware of the importance of SRL for their students, they often find it difficult to implement SRL opportunities in their teaching. To support teacher professional development, an SRL model was described in a previous theoretical study. In the present article, this SRL model is elaborated towards the ‘SRL Opportunities Questionnaire’ (SRLOQ) that can be applied by primary teacher educators as a diagnostic instrument for classroom settings. A four-phase research design is applied consisting of scale development, score validation, further validation of the SRLOQ in primary teacher education, and a confirmatory factor analysis. Finally, a single case study is described that illustrates the usefulness of the SRLOQ in classroom practice

Stochastic nash equilibrium problems: sample average approximation and applications

This paper presents a Nash equilibrium model where the underlying objective functions involve uncertainty and nonsmoothness. The well-known sample average approximation method is applied to solve the problem and the first order equilibrium conditions are characterized in terms of Clarke generalized gradients. Under some moderate conditions, it is shown that with probability one, a statistical estimator (a Nash equilibrium or a Nash-C-stationary point) obtained from sample average approximate equilibrium problem converges to its true counterpart. Moreover, under some calmness conditions of the Clarke generalized derivatives, it is shown that with probability approaching one exponentially fast by increasing sample size, the Nash-C-stationary point converges to a weak Nash-C-stationary point of the true problem. Finally, the model is applied to stochastic Nash equilibrium problem in the wholesale electricity market