Modelling risk and uncertainty with the analytic hierarchy process

This paper proposes methods for modelling risk and uncertainty with the analytic hierarchy process (AHP). We start by showing why benefit/risk ratios, as described in previous literature, might be an improper modelling approach. We then introduce prototypical case studies where risk plays a role in multicriteria decision making. These cases demonstrate how the AHP can be used to derive relative probabilities, multiple criteria outcome measures, risk criteria, and risk adjustment factors. Copyright © 2003 John Wiley & Sons, Ltd.     

The relation between goal adjustment,goal disturbance,and mental well-being among persons with multiple sclerosis

Objective: This study investigated the role of goal adjustment, i.e. disengaging from blocked goals and reengaging into alternative goals, in mental well-being and goal disturbance in persons with multiple sclerosis (MS).

Design: A cross-sectional design was used with self-report data from questionnaires and Personal Project Analysis (PPA).

Main outcome measures: Dependent variables were mental well-being, indicated by depression/anxiety (HADS; Hospital Anxiety and Depression Scale) and mental functioning (SF-36; Short Form Health Survey), and goal disturbance, indicated by goal manageability and goal interference (PPA). Independent variables were patient-reported physical impairment (SF-36) and goal disengagement and reengagement (GAS; Goal Adjustment Scale).

Results: Higher goal reengagement was associated with better mental well-being, but unrelated to goal disturbance. Goal disengagement only showed a negative association with anxiety. High disengagement was associated with lower goal interference but only for those also scoring high on reengagement. Goal adjustment did not buffer the effects of physical impairment on mental well-being and goal disturbance. Contrary to expectations, higher goal reengagement increased the association between physical impairment and goal interference.

Conclusion: Although goal reengagement is associated with better mental well-being in persons with MS, it might also strengthen the perceived effect of physical impairment on goal interference.     

Multiple objective programming with piecewise linear functions

An approach to generating all efficient solutions for multiple objective programs with piecewise linear objective functions and linear constraints is presented. The approach is based on the decomposition of the feasible set into subsets, referred to as cells, so that the original problem reduces to a series of single objective linear programs and feasibility tests over the cells. The concepts of cell-efficiency and complex-efficiency are introduced and their relationship with efficiency is examined. A generic algorithm for finding efficient solutions for bi-objective piecewise linear programs is proposed. Applications in location theory as well as in worst case analysis are highlighted. Copyright © 1999 John Wiley & Sons, Ltd.