Indicators for the characterization of discrete Choquet integrals

Belles-Sampera, Jaume; Merigó, José M.; Guillén, Montserrat; Santolino, Miguel

doi:10.1016/j.ins.2014.01.047

Cited by 25 publications

(10 citation statements)

References 41 publications

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“…One way in which to describe the characteristics of discrete Choquet integrals is to use a set of aggregation indicators, which provide information about features of the underlaying aggregation operator (7) . Here, we investigate the quantitative information related to the overall risk attitude associated with the risk measure as provided by the aggregation indicators.…”

Section: Attitude Towards Riskmentioning

confidence: 99%

What attitudes to risk underlie distortion risk measure choices?

Belles-Sampera

Guillén

Santolino

2016

Insurance: Mathematics and Economics

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Understanding the attitude to risk implicit within a risk measure sheds some light on the way in which decision makers perceive losses. In this paper, a two-stage strategy is developed to characterize the underlying risk attitude involved in a risk evaluation, when executed by the family of distortion risk measures. First, we show that aggregation indicators defined for discrete Choquet integrals provide information about the implicit global risk attitude of the agent. Second, an analysis of the distortion function offers a local description of the agent's stance on risk in relation to the occurrence of accumulated losses. Here, the concepts of absolute risk attitude and local risk attitude arise naturally. An example is provided to illustrate the usefulness of this strategy for characterizing risk attitudes in an insurance company.

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Section: Attitude Towards Riskmentioning

confidence: 99%

What attitudes to risk underlie distortion risk measure choices?

Belles-Sampera

Guillén

Santolino

2016

Insurance: Mathematics and Economics

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“…Degree of balance, the divergence, the variance indicator and Re'nyi entropies are four indicators usually associated with the OWA aggregator. Belles-Sampera et al [5] extended these indicators to discrete Choquet integrals.…”

Section: Choquet Integral Emphasizing On Mcdm Problemsmentioning

confidence: 99%

Fuzzified Choquet Integral and its Applications in MADM: A Review and A New Method

Keikha

Nehi

2015

Int. J. Fuzzy Syst.

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Aggregation of information using Choquet integral method, caused to interdependent or interactive characteristics among the decision maker's preference criteria also considered. In this paper, after introducing Choquet integral as a powerful aggregation function, some existing fuzzified Choquet integral methods will be reviewed. Then, we propose a new method for aggregation of fuzzy-valued information using Choquet integral and compare it with others. This method preserves the properties of fuzzy numbers, that is, the resulting data are the same type as the early data. So, ranking of such numbers, which is necessary in multi attribute decision-making (MADM) problems, was performed using ranking methods of fuzzy numbers. Also, we will apply the proposed method in both single and group decision-making problems to solve MADM problems, while the evaluation values and then decision matrix are fuzzy numbers.

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“…In particular, if µ(F ) = |F | n , for all F ⊆ X, then both the GDHFCOG operator in Equation (36) and the GDHFOWG operator in Equation (39) reduce to the GDHFG operator, which is shown in Equation (38).…”

Section: Definition 12mentioning

confidence: 99%

“…However, more correlations are required to be considered in the decision making process due to the interdependent among attributes in practical applications. The Choquet integral, originally developed by Choquet [34], provides an approach to process the inter-dependence or correlation among attributes [35][36][37][38][39][40][41][42][43][44][45]. Although some hesitant fuzzy Choquet integral aggregation operators, such as the hesitant fuzzy Choquet ordered averaging (HFCOA) operator, the hesitant fuzzy Choquet ordered geometric (HFCOG) operator, the generalized hesitant fuzzy Choquet ordered averaging (GHFCOA) operator, the generalized hesitant fuzzy Choquet ordered geometric (GHFCOG) operator [24], the hesitant fuzzy linguistic correlated averaging (HFLCA) operator, the hesitant fuzzy linguistic correlated geometric (HFLCG) operator [46] and the hesitant fuzzy Choquet integral (HFCI) operator [47], have been proposed to deal with MADM problems under hesitant fuzzy environment, they fail to solve the MADM problems with dual hesitant fuzzy information.…”

Section: Introductionmentioning

confidence: 99%

Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making

Yang

Liu

2014

Journal of Intelligent &Amp; Fuzzy Systems

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With respect to multiple attribute decision making (MADM) problems in which the attributes are inter-dependent and take the form of dual hesitant fuzzy elements, a new MADM method with dual hesitant fuzzy information is investigated in this paper. Firstly, by using the Choquet integral, some new aggregation operators are developed for aggregating the dual hesitant fuzzy information, such as the dual hesitant fuzzy Choquet ordered average (DHFCOA) operator, the dual hesitant fuzzy Choquet ordered geometric (DHFCOG) operator, the generalized dual hesitant fuzzy Choquet ordered average (GDHFCOA) operator and the generalized dual hesitant fuzzy Choquet ordered geometric (GDHFCOG) operator. Then, some special cases, desirable properties of these operators and the relationships between them are discussed. Furthermore, based on the DHFCOA operator, an approach to MADM is proposed under dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

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Indicators for the characterization of discrete Choquet integrals

Cited by 25 publications

References 41 publications

What attitudes to risk underlie distortion risk measure choices?

What attitudes to risk underlie distortion risk measure choices?

Fuzzified Choquet Integral and its Applications in MADM: A Review and A New Method

Some new dual hesitant fuzzy aggregation operators based on Choquet integral and their applications to multiple attribute decision making

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