Between Science and Democracy : the Role of “ Social Multi - Criteria Evaluation ( SMCE ) ” by Giuseppe Munda

The additivity property of the ``measure'', one of the most important concepts in mathematics, is often inflexible or too rigid to represent the many facets of human reasoning. In order to be able to express human subjectivity, recent researches proposed to replace this property by a weaker one, the ``monotonicity'' and called these non-additive monotonic measures ``fuzzy measures''. “Fuzzy integral” is a generic term for integrals with respect to fuzzy measures. In this thesis we will mainly concentrate on the Choquet integral. This integral provides an alternative scheme to aggregate the information. Indeed, this aggregation operator, in the evaluation process, takes into account, not only the importance of each criterion but also the importance of all subsets of criteria. Most multicriteria decision aid methods are based on an aggregation procedure. The most commonly used aggregation operators must satisfy the independence assumption. Nevertheless, there are few cases where this supposition is verified, and in this case, we talk about the interactions between criteria. The originality of our research is based on the introduction of these concepts of fuzzy measures and integrals into the multicriteria sorting methods. Indeed, the Choquet integral allows to take into account the importance of each criterion as well as the interactions of synergy and redundancy between them. The proposed methods are implemented and tested on the Diagnostic of Firms Problem: The financial information, widely used in the assessment of a firm presents a high degree of dependences and these interactions have an influence on the financial position of the firm. The methodology proposed in this thesis allows to take into account these relations of synergy and redundancy between the analysed criteria in the evaluation process.