Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences

"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

Ambiguity and Social Interaction

We examine the impact of ambiguity on economic behaviour. We present a relatively non-technical account of ambiguity and show how it may be applied in economics. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. We also examine the effects of ambiguity on peace processes. It is shown that ambiguity can act to select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements.

Sequential Two-Player Games with Ambiguity

If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.

A Multicriteria Approach for the Evaluation of the Sustainability of Re-use of Historic Buildings in Venice

The paper presents a multiple criteria model for the evaluation of the sustainability of projects for the economic re-use of historical buildings in Venice. The model utilises the relevant parameters for the appraisal of sustainability, aggregated into three macro-indicators: intrinsic sustainability, context sustainability and economic-financial feasibility. The model has been calibrated by a panel of experts and tested on two reuse hypotheses of the Old Arsenal in Venice. The tests have proven the model to be a useful support in the early stages of evaluation of re-use projects, where economic improvements are to be combined with conservation, as it supports the identification of critical points and the selection of projects, thus providing not only a check-list of variables to be considered, but an appraisal of trade-offs between economic uses and requirements of conservation.Economic Reuse, Historical Building Conservation

Insights and Characterization of l1-norm Based Sparsity Learning of a Lexicographically Encoded Capacity Vector for the Choquet Integral

This thesis aims to simultaneously minimize function error and model complexity for data fusion via the Choquet integral (CI). The CI is a generator function, i.e., it is parametric and yields a wealth of aggregation operators based on the specifics of the underlying fuzzy measure. It is often the case that we desire to learn a fusion from data and the goal is to have the smallest possible sum of squared error between the trained model and a set of labels. However, we also desire to learn as “simple’’ of solutions as possible. Herein, L1-norm regularization of a lexicographically encoded capacity vector relative to the CI is explored. The impact of regularization is explored in terms of what capacities and aggregation operators it induces under different common and extreme scenarios. Synthetic experiments are provided in order to illustrate the propositions and concepts put forth

On the use of the Choquet Integral for the Collaborative Creation of Learning Objects

Computer-supported collaborative knowledge creation is the continuous process of development of knowledge assets, where produced knowledge has to be assessed by the developers, taking into account a set of criteria that may keep some interdependencies. This work poses an approach for collaborative creation of learning objects in a Web-based, educational context, based upon a coordination protocol and an aggregation mechanism. The coordination protocol allows the continuous consolidation of opinions issued about the learning objects produced by a number of authors. During certain steps of the protocol, an aggregation process is performed that takes into account the inter-dependence among criteria. The results of using the Choquet integral as an aggregation operator are compared to the usual aggregation procedure based upon weighted arithmetic means

Assessing payment instrument alternatives using cognitive mapping and the choquet integral

Technological advances have increased the diversity of payment instruments and transaction channels, heightening consumers' expectations for services in this regard. Coupled with an increasing competitiveness of the banking industry, this has emphasized the great importance of understanding consumers' choices of payment instruments. In order to meet their customers' expectations, banks have to understand what determines their choices of payment instruments. This study aims to uncover these determinants of payment instrument choice, through the use of cognitive mapping to structure the decision problem, and its combination with the Choquet integral to identify the overall preferred payment instrument from the user perspective. The results show that direct debits and electronic cards constitute the preferred payment instruments, and automated teller machines (ATMs) and point-of-sale (POS) the overall preferred transaction channels. Understanding consumers' choices of payment instrument, the factors underlying them and their interactions can contribute to better planning by banks at the distribution channel level. Strengths, limitations and managerial implications of our proposal are also discussed.info:eu-repo/semantics/publishedVersio