Computing Choquet integrals

Chiţescu, Ion; Plǎviţu, Anca

doi:10.1016/j.fss.2017.02.009

Cited by 9 publications

(3 citation statements)

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“…Fuzzy measures and integrals are useful tools for describing nonadditive phenomena. Additivity can express a noninteraction or indifference, whereas nonadditivity has the ability to express the interactions among the contribution rates of points in a universal set (Chiţescu and Plăviţu 2017). The above analysis has encouraged us to apply nonadditive measures for quantifying the positive and negative synergistic effects in our decision-making scenario.…”

Section: Preliminariesmentioning

confidence: 99%

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A regional Natech risk assessment based on a Natech-prone facility network for dependent events

Cai

Marson

2021

Nat Hazards

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Because of the recent frequency of climatic hazards and extreme weather events, disasters caused by natural hazards are attracting increased attention from the governments, communities, and the public. Synergistic effects between natural and technological hazards have a significant role in risk assessment. To address these effects, a Natech risk assessment model based on a natural-technological-prone (Natech-prone) facility network is developed to clarify specific scenarios and assess Natech risk. A weighted and directed graph is employed to map out the industrial facilities and other necessary information emerging from the display. It is assumed that the final risk triggered by a natural event is the result of disasters caused by Natech-prone facilities. The decision weights of Natech-prone facilities are heavily dependent on the recognition of the interacting components. A subjective probability is applied to the expected risk utility function to overcome the disadvantage of objective probability, which fails to address the uncertainty found in irrational human factors. Fuzzy measures are used to describe the positive and negative synergistic effects caused by the interaction between Natech-prone facilities. In addition, a Choquet integral is incorporated into the method to deduce the positive and negative synergistic effects in risk assessment. A numerical example is given to illustrate the model, and comparisons and analyses are provided. This paper conceptualizes a specific scenario of a Natech accident. The use of an expected risk utility function for dependent disaster events is a new idea in the field of Natech risk assessment.

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Section: Preliminariesmentioning

confidence: 99%

“…These human factors cause positive or negative synergistic effects in a risk assessment and make the decision-making problem more difficult to overcome (Agani et al 2010). Cai and Wei (2020) constructed a social vulnerability evaluation index system from the perspective of disaster bearers.…”

Section: Introductionmentioning

confidence: 99%

A regional Natech risk assessment based on a Natech-prone facility network for dependent events

Cai

Marson

2021

Nat Hazards

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“…According to Lebesgue’s philosophy [10], once a measure is defined, it is possible to obtain an integral with regard to that measure. Thus, associated with the concept of fuzzy measure , there is the concept of fuzzy integral [11, 12], being the Choquet integral one of the most popular [13–17]. The Choquet integral constitutes a generalization of the Lebesgue integral [10], as well as of other traditional operators (e.g.…”

Section: Introductionmentioning

confidence: 99%

Choquet integral-based fuzzy molecular characterizations: when global definitions are computed from the dependency among atom/bond contributions (LOVIs/LOEIs)

et al. 2018

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BackgroundSeveral topological (2D) and geometric (3D) molecular descriptors (MDs) are calculated from local vertex/edge invariants (LOVIs/LOEIs) by performing an aggregation process. To this end, norm-, mean- and statistic-based (non-fuzzy) operators are used, under the assumption that LOVIs/LOEIs are independent (orthogonal) values of one another. These operators are based on additive and/or linear measures and, consequently, they cannot be used to encode information from interrelated criteria. Thus, as LOVIs/LOEIs are not orthogonal values, then non-additive (fuzzy) measures can be used to encode the interrelation among them.ResultsGeneral approaches to compute fuzzy 2D/3D-MDs from the contribution of each atom (LOVIs) or covalent bond (LOEIs) within a molecule are proposed, by using the Choquet integral as fuzzy aggregation operator. The Choquet integral-based operator is rather different from the other operators often used for the 2D/3D-MDs calculation. It performs a reordering step to fuse the LOVIs/LOEIs according to their magnitudes and, in addition, it considers the interrelation among them through a fuzzy measure. With this operator, fuzzy definitions can be derived from traditional or recent MDs; for instance, fuzzy Randic-like connectivity indices, fuzzy Balaban-like indices, fuzzy Kier–Hall connectivity indices, among others. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS 3D-MDs were used as study case and, as a result, a module was built into the corresponding software to compute them (http://tomocomd.com/qubils-midas). Thus, it is the only software reported in the literature that can be employed to determine Choquet integral-based fuzzy MDs. Moreover, regression models were created on eight chemical datasets. In this way, a comparison between the results achieved by the models based on the non-fuzzy QuBiLS-MIDAS 3D-MDs with regard to the ones achieved by the models based on the fuzzy QuBiLS-MIDAS 3D-MDs was made. As a result, the models built with the fuzzy QuBiLS-MIDAS 3D-MDs achieved the best performance, which was statistically corroborated through the Wilcoxon signed-rank test.ConclusionsAll in all, it can be concluded that the Choquet integral constitutes a prominent alternative to compute fuzzy 2D/3D-MDs from LOVIs/LOEIs. In this way, better characterizations of the compounds can be obtained, which will be ultimately useful in enhancing the modelling ability of existing traditional 2D/3D-MDs.Electronic supplementary materialThe online version of this article (10.1186/s13321-018-0306-7) contains supplementary material, which is available to authorized users.

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