Necessary and possible interaction between criteria in a 2-additive Choquet integral model

Mayag, Brice; Bouyssou, Denis

doi:10.1016/j.ejor.2019.10.036

Cited by 28 publications

(32 citation statements)

References 48 publications

(74 reference statements)

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“…This result shows that positive synergy interaction is always possible for all pairs of criteria in a 2-maxitive Sugeno integral model if the ordinal information does not contain indifference. This condition is the same as that obtained in the case of the 2-additive Choquet integral [14].…”

Section: Resultsmentioning

confidence: 59%

“…Indeed, this interaction is strictly positive (see Cap. Depending on the numerical representation µ, the interaction index can be null or strictly positive, this led to the definition of the notion of necessary and possible interaction, as introduced in [12,14] for the Choquet integral model.…”

Section: A Motivating Examplementioning

confidence: 99%

“…In [14], it is proven that in the framework of binary alternatives, if the preferential information contains no indifference, and if it is representable by a 2additive Choquet integral model, then it is always possible to represent these preferences by a strict positive interaction. We obtain a similar result with the 2-maxitive Sugeno integral.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model

Kaldjob

Mayag

Bouyssou

2021

Algorithmic Decision Theory

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This paper proposes and studies the notion of interaction between two criteria in a 2-maxitive Sugeno integral model. Within the framework of binary alternatives, we give a necessary and sufficient condition for preferential information on binary alternatives to be representable by a 2-maxitive Sugeno integral model. Using this condition, we show that it is always possible to choose a numerical representation, for which all the interaction indices are strictly positive. Outside the framework of binary alternatives, by introducing of binary variables, we propose a MILP allowing to test whether an ordinal preference information is representable by a 2-maxitive Sugeno integral model and whether the interpretation of the interaction indices is ambiguous or not. We illustrate our results with examples.

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Section: Resultsmentioning

confidence: 59%

Section: A Motivating Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model

Kaldjob

Mayag

Bouyssou

2021

Algorithmic Decision Theory

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show abstract

“…However, because the interaction between attributes is difficult to explain and understand [8], combined with the uncertainty of decision-makers' cognition, the decision-makers often cannot give accurate quantitative assessment on the interactivity between attributes, but with a certain fuzziness and hesitation, which brings difficulties to decisionmaking. The existing 2-order additive fuzzy measure identification methods use the subjective methods [9][10][11][12][13][14][15] and the objective methods [7,16,17] to describe and deal with the interactivity between attributes.…”

Section: Introductionmentioning

confidence: 99%

A 2-order additive fuzzy measure identification method based on intuitionistic fuzzy sets and its application in credit evaluation

Zhang

Zhao

2021

IFS

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In view of the problem that it is difficult to quantitatively assess the interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the intuitionistic fuzzy sets (IFSs) to describe and deal with the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. On this basis, the experts employ the intuitionistic fuzzy number (IFN) to assess the interactivity between attributes, Secondly, the opinions of all experts are aggregated by using the intuitionistic fuzzy weighted average operator (IFWA). Finally, based on the aggregated results, the intuitionistic fuzzy interaction degree between attributes is defined and calculated by the score function of IFN. Thus, a 2-order additive fuzzy measure identification method based on IFSs is further proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is presented. Taking the credit evaluation of the big data listed companies in China as an application example, the feasibility and effectiveness of the proposed method is verified by the analysis results of application example.

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“…Indeed, our first result gives a necessary and sufficient condition for preferential information on generalized binary alternatives to be representable by a general model of Choquet integral. In [5] it is proven that in the framework of binary alternatives, if the preferential information contains no indifference, and is representable by a 2-additive Choquet model, then we can choose among these representations one for which all Shapley interaction indices between two criteria are strictly positive. We extend also this result.…”

Section: Introductionmentioning

confidence: 99%

Necessary and Possible Interaction Between Criteria in a General Choquet Integral Model

Kaldjob¹,

Mayag²,

Bouyssou³

2020

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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This paper deals with interaction between criteria in a general Choquet integral model. When the preference of the Decision Maker (DM) contains no indifference, we first give a necessary and sufficient condition for them to be representable by a Choquet integral model. Using this condition, we show that it is always possible to choose from the numerical representations, one relatively for which all the Shapley interaction indices are strictly positive. We illustrate our results with an example.

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Necessary and possible interaction between criteria in a 2-additive Choquet integral model

Cited by 28 publications

References 48 publications

Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model

Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model

A 2-order additive fuzzy measure identification method based on intuitionistic fuzzy sets and its application in credit evaluation

Necessary and Possible Interaction Between Criteria in a General Choquet Integral Model

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