Sorting multiattribute alternatives: The TOMASO method

in Computers and Operations Research (2005), 32(4), 861-877

We analyze a recently proposed ordinal sorting procedure (Tomaso) for the assignment of alternatives to graded classes and we present a freeware constructed from this procedure. We illustrate it by two ... [more ▼]

We analyze a recently proposed ordinal sorting procedure (Tomaso) for the assignment of alternatives to graded classes and we present a freeware constructed from this procedure. We illustrate it by two examples, and do some testing in order to show its usefulness. [less ▲]

TOMASO, A solution in the presence of interacting points of views

Article for general public (2004)

This short article briefly presents the main features of the multiple criteria sorting tool TOMASO (Technique for Ordinal Multi-Attribute Sorting and Ordering) and its implementation. Its main ... [more ▼]

This short article briefly presents the main features of the multiple criteria sorting tool TOMASO (Technique for Ordinal Multi-Attribute Sorting and Ordering) and its implementation. Its main particularities are the possibility to consider interacting points of view and the use of the Choquet integral as a discriminant function. The capacities are learnt through the use of protoypes, which are well known alternatives for the Decision Maker. [less ▲]

The use of the discrete Sugeno integral in decision making: a survey

in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems (2001), 9(5), 539-561

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a preference functional is presented in the qualitative framework of two decision paradigms: multi-criteria decision ... [more ▼]

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a preference functional is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making and decision-making under uncertainty. The parallelism between the representation theorems in both settings is stressed, even if a basic requirement like the idempotency of the aggregation scheme should be explicitely stated in multi-criteria decision-making, while its counterpart is implicit in decision under uncertainty by equating the utility of a constant act with the utility of its consequence. Important particular cases of Sugeno integrals such as prioritized minimum and maximum operators, their ordered versions, and Boolean max-min functions are studied. [less ▲]

The use of the discrete Sugeno integral in decision making: a survey

in Colorni, A.; Paruccini, M.; Roy, B. (Eds.) AMCDA - Aide Multi Critère à la Décision (Multiple Criteria Decision Aiding) (2001)

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a utility function is presented in the qualitative framework of two decision paradigms: multi-criteria decision ... [more ▼]

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a utility function is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making and decision-making under uncertainty. The parallelism between the representation theorems in both settings is stressed, even if a basic requirement like idempotency should be explicitely stated in multi-criteria decision-making, while its counterpart is implicit in decision under uncertainty by equating the utility of a constant act with the utility of its consequence. Important particular cases of Sugeno integrals such as prioritized minimum and maximum operators, their ordered versions, and Boolean max-min functions are studied. [less ▲]

Entropy of discrete fuzzy measures

in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems (2000), 8(6), 625-640

The concept of entropy of a discrete fuzzy measure has been recently introduced in two different ways. A first definition was proposed by Marichal in the aggregation framework, and a second one by Yager ... [more ▼]

The concept of entropy of a discrete fuzzy measure has been recently introduced in two different ways. A first definition was proposed by Marichal in the aggregation framework, and a second one by Yager in the framework of uncertain variables. We present a comparative study between these two proposals and point out their properties. We also propose a definition for the entropy of an ordinal fuzzy measure, that is, a fuzzy measure taking its values in an ordinal scale in the sense of measurement theory. [less ▲]

On the entropy of non-additive weights

Scientific Conference (2000, July)

We consider a Choquet capacity, that is a set function which describes the importance of every subset of criteria in a MCDA problem. The following question is approached: what is the generalized ... [more ▼]

We consider a Choquet capacity, that is a set function which describes the importance of every subset of criteria in a MCDA problem. The following question is approached: what is the generalized counterpart of the Shannon entropy (defined for a probabilistic measure) for such a capacity? The extension that is proposed depends on the scale type. In the cardinal case, the entropy is defined in terms of the first derivatives of the non-additive measures. In the ordinal case, it refers to the cardinality of the scale values that appear in the set of all capacities. Both generalized entropies are symmetric functions of the capacities and their extreme values (max entropy and min entropy) are characterized. An application to the determination of weights is given when interacting criteria are considered. [less ▲]

Equivalent representations of set functions

in Mathematics of Operations Research (2000), 25(2), 157-178

This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as ... [more ▼]

This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation. [less ▲]

Aide à la décision en présence de données ordinales

Presentation (1999, October 22)

Consensus with ordinal data

in Proc. 7th Eur. Congr. on Intelligent Techniques and Soft Computing (EUFIT'99) (1999, September)

We present a model allowing to aggregate decision criteria when the available information is of qualitative nature. The use of the Sugeno integral in this model is justified by an axiomatic approach. An ... [more ▼]

We present a model allowing to aggregate decision criteria when the available information is of qualitative nature. The use of the Sugeno integral in this model is justified by an axiomatic approach. An illustrative example is also provided. [less ▲]

About the Choquet integral as a tool to aggregate utilities in the presence of interacting points of view

Scientific Conference (1999, August)

One basic assumption to consider an additive utility function is the preferential independence. When interacting criteria are considered, this condition might be violated and a substitute to the classical ... [more ▼]

One basic assumption to consider an additive utility function is the preferential independence. When interacting criteria are considered, this condition might be violated and a substitute to the classical weighted mean has to be adopted. The Choquet integral seems to be an adequate aggregation operator that extends the weighted mean and the ordered weighted average (OWA). The axiomatics that supports the Choquet integral is presented as well as its behavioral analysis with regards to veto and favor effects, degree of disjunction and measure of dispersion. One illustrative example of its application in the field of MCDM is provided. [less ▲]