A characterization of the 2-additive Choquet integral through cardinal information

Mayag, Brice; Grabisch, Michel; Labreuche, Christophe

doi:10.1016/j.fss.2010.10.012

Cited by 50 publications

(28 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The MOPI condition given in this paper is in fact equivalent to the more complex MOPI property presented in Mayag et al [2008]. We give below the main result of the paper which is a theorem of characterization of consistent ordinal information {P, I} representable by a 2-additive Choquet integral: Theorem 1 characterizes the 2-additive Choquet integral in terms of preference, and shows that only two types of inconsistencies can occur in an ordinal information given by a DM in order to represent it by a 2-additive Choquet integral.…”

mentioning

confidence: 96%

A representation of preferences by the Choquet integral with respect to a 2-additive capacity

2010

Self Cite

View full text Add to dashboard Cite

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI. Abstract In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

show abstract

mentioning

confidence: 96%

A representation of preferences by the Choquet integral with respect to a 2-additive capacity

2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…According to Mayag et al (2011), given (x 1 , x 2 , …, x n ) the individual utilities for the different measures, the CI with respect to a two-additive capacity can be written as follows:…”

Section: General Methodologymentioning

confidence: 99%

Development of a multi-criteria evaluation system to assess growing pig welfare

Martin¹,

Traulsen²,

Buxadé

et al. 2017

Animal

View full text Add to dashboard Cite

The aim of this paper was to present an alternative multi-criteria evaluation model to assess animal welfare on farms based on the Welfare Quality ® (WQ) project, using an example of welfare assessment of growing pigs. The WQ assessment protocol follows a three-step aggregation process. Measures are aggregated into criteria, criteria into principles and principles into an overall assessment. This study focussed on the first step of the aggregation. Multi-attribute utility theory (MAUT) was used to produce a value of welfare for each criterion. The utility functions and the aggregation function were constructed in two separated steps. The Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) method was used for utility function determination and the Choquet Integral (CI) was used as an aggregation operator. The WQ decision-makers' preferences were fitted in order to construct the utility functions and to determine the CI parameters. The methods were tested with generated data sets for farms of growing pigs. Using the MAUT, similar results were obtained to the ones obtained applying the WQ protocol aggregation methods. It can be concluded that due to the use of an interactive approach such as MACBETH, this alternative methodology is more transparent and more flexible than the methodology proposed by WQ, which allows the possibility to modify the model according, for instance, to new scientific knowledge.

show abstract

“…With this methodology, a progressive interactive approach can be developed after an initial calculation of the CI, where additional constraints to the Shapley values, which measure the overall importance of a measure (criterion), and the interaction indices can be imposed in order to fit more precisely the WQ DMs preferences. According to Mayag et al (2011), given (x 1 , x 2 , … , x n ) the individual utilities for the different measures, the CI with respect to a two-additive capacity can be written as follows:…”

Section: Datamentioning

confidence: 99%

Validation of a multi-criteria evaluation model for animal welfare

Martin¹,

Czycholl²,

Buxadé

et al. 2017

Animal

View full text Add to dashboard Cite

The aim of this paper was to validate an alternative multi-criteria evaluation system to assess animal welfare on farms based on the Welfare Quality ® (WQ) project, using an example of welfare assessment of growing pigs. This alternative methodology aimed to be more transparent for stakeholders and more flexible than the methodology proposed by WQ. The WQ assessment protocol for growing pigs was implemented to collect data in different farms in Schleswig-Holstein, Germany. In total, 44 observations were carried out. The aggregation system proposed in the WQ protocol follows a three-step aggregation process. Measures are aggregated into criteria, criteria into principles and principles into an overall assessment. This study focussed on the first two steps of the aggregation. Multi-attribute utility theory (MAUT) was used to produce a value of welfare for each criterion and principle. The utility functions and the aggregation function were constructed in two separated steps. The MACBETH (Measuring Attractiveness by a Categorical-Based Evaluation Technique) method was used for utility function determination and the Choquet integral (CI) was used as an aggregation operator. The WQ decision-makers' preferences were fitted in order to construct the utility functions and to determine the CI parameters. The validation of the MAUT model was divided into two steps, first, the results of the model were compared with the results of the WQ project at criteria and principle level, and second, a sensitivity analysis of our model was carried out to demonstrate the relative importance of welfare measures in the different steps of the multi-criteria aggregation process. Using the MAUT, similar results were obtained to those obtained when applying the WQ protocol aggregation methods, both at criteria and principle level. Thus, this model could be implemented to produce an overall assessment of animal welfare in the context of the WQ protocol for growing pigs. Furthermore, this methodology could also be used as a framework in order to produce an overall assessment of welfare for other livestock species. Two main findings are obtained from the sensitivity analysis, first, a limited number of measures had a strong influence on improving or worsening the level of welfare at criteria level and second, the MAUT model was not very sensitive to an improvement in or a worsening of single welfare measures at principle level. The use of weighted sums and the conversion of disease measures into ordinal scores should be reconsidered.

show abstract

A characterization of the 2-additive Choquet integral through cardinal information

Cited by 50 publications

References 34 publications

A representation of preferences by the Choquet integral with respect to a 2-additive capacity

A representation of preferences by the Choquet integral with respect to a 2-additive capacity

Development of a multi-criteria evaluation system to assess growing pig welfare

Validation of a multi-criteria evaluation model for animal welfare

Contact Info

Product

Resources

About