Towards sustainability: An assessment of an urbanisation bubble in China using a hierarchical - stochastic multicriteria acceptability analysis - Choquet integral method

Urbanisation bubbles have become an increasingly serious problem. Attention has been paid to the speed of urbanisation; however, the issue of quality has been neglected, particularly in the case of China. Therefore, the aim of this research is to evaluate China’s urbanisation bubbles by employing a hierarchical - stochastic multicriteria acceptability analysis (SMAA) - Choquet integral method. In order to highlight regional disparities, we measure the urbanisation bubbles at a provincial level. Our study aggregates the urbanisation bubble indices using the Choquet integral preference model, and considers the interactions between various indicators. Furthermore, robust ordinal regression and SMAA are applied to resolve the robustness issues associated with the entire set of weights assigned to the urbanisation bubble composite indicator. In addition, by employing a multiple criteria hierarchy process, the study aggregates urbanisation bubble indices not only at the comprehensive level, but also at the intermediate levels of the hierarchy. Our findings suggest that the ranking of urbanisation bubbles is positively related to the level of regional development. This study contributes to the evaluation of regional urbanisation and sustainable development

Implementations of PACMAN

Passive and Active Compensability Multicriteria ANalysis (PACMAN) is a multiple criteria methodology based on a decision maker oriented notion of compensation, called compensability. An important feature of PACMAN is a possible asymmetry of the connected decision procedure, since compensability is determined for each ordered pair of criteria, distinguishing the compensating criterion from the compensated one. Here we give a notion of implementation of PACMAN, which allows a concrete modelization of a multiple criteria decision problem. We study regular implementations of PACMAN and their monotonicity properties. We also examine several regular implementations, which satisfy some additional properties. Particular emphasis is given to a regular implementation of PACMAN that produces the lexicographic ordering.Multiple criteria analysis Pairwise criterion comparison approach Compensability Dominance Lexicographic ordering

Non-additive robust ordinal regression with Choquet integral, bipolar and level dependent

Choquet integral

A linear implementation of PACMAN

PACMAN (Passive and Active Compensability Multicriteria ANalysis) is a multiple criteria methodology based on a decision maker oriented notion of compensation, called compensability. A basic step of PACMAN is the construction of compensatory functions, which model intercriteria relations for each pair of criteria on the basis of compensability. In this paper we examine a simplified version of PACMAN, which uses the so-called linear compensatory functions and consistently reduces the overall complexity of its implementation in practical cases. We use Mathematica® to develop a computer-aided graphical interface that eases the interaction among the actors of the decision process at each stage of PACMAN. We also propose the possibility to perform a sensitivity analysis in this simplified version of PACMAN as a nonlinear optimization problem.C00 D00 D81 Multiple criteria analysis Pairwise criterion comparison approach Compensation Compensability analysis Compensatory function Sensitivity analysis

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Within the multicriteria aggregation-disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM's preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM's preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach. In our methodology, besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives A'[subset, double equals]A, the DM is also requested to express the intensity of preference on pairs of alternatives from A', and to supply pairwise comparisons on the importance of criteria, and the sign and intensity of interaction among pairs of criteria. The output of our approach defines a set of fuzzy measures (capacities) such that the corresponding Choquet integral is compatible with the DM's preference information. Moreover, using linear programming, our decision model establishes two preference relations for any a,b[set membership, variant]A: the necessary weak preference relation, if for all compatible fuzzy measures the utility of a is not smaller than the utility of b, and the possible weak preference relation, if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b.Multiple criteria decision analysis Interacting criteria Choquet integral Non-additive robust ordinal regression Aggregation-disaggregation approach