Fuzzy-statistical prediction intervals from crisp regression models

Adjenughwure, Kingsley; Papadopoulos, Basil K.

doi:10.1007/s12530-019-09285-6

Cited by 9 publications

(13 citation statements)

References 20 publications

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“…We can interpret the ⟨α, β⟩-cuts of reserves (Tables 11 and 12) as similar to probabilistic intervals (Table 8). The equivalence between the α-cuts of possibility distributions and probabilistic confidence intervals has been extensively documented in the literature on probability-possibility transformations [64][65][66][67]. In this regard, it should be emphasized that the β-cut of the nonmembership function of an IFN can be interpreted as the (1 − β) of the upper possibility function [32].…”

Section: Significancementioning

confidence: 90%

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

De Andrés-Sánchez

2024

Axioms

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A highly relevant topic in the actuarial literature is so-called “claim reserving” or “loss reserving”, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate these reserves and their variability. Regression methods are widely used in this setting. If we model error terms as random variables, the variability of provisions can consequently be modelled stochastically. The use of fuzzy regression methods also allows modelling uncertainty for reserve values using tools from the theory of fuzzy subsets. This study follows this second approach and proposes projecting claim reserves using a generalization of fuzzy numbers (FNs), so-called intuitionistic fuzzy numbers (IFNs), through the use of intuitionistic fuzzy regression. While FNs allow epistemic uncertainty to be considered in variable estimation, IFNs add bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis is grounded in the ANOVA two-way framework, which is adapted to the use of intuitionistic regression. Similarly, we compare our results with those obtained using deterministic and stochastic chain-ladder methods and those obtained using two-way statistical ANOVA.

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Section: Significancementioning

confidence: 90%

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

De Andrés-Sánchez

2024

Axioms

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“…It should be emphasized that the interpretation of probabilistic confidence intervals as α-level sets of possibility distributions has been widely argued in the literature [53,54,[56][57][58][59][60][61]. Buckley [58] justified the transformation of a set of probabilistic confidence intervals into fuzzy numbers with the fact that in subsequent calculations, more information is used than simple point estimates or confidence intervals.…”

Section: Methods To Fit Fuzzy Parameters Note Extensions Taylor's Sep...mentioning

confidence: 99%

Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

Andrés-Sánchez

2024

Mathematics

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Estimating loss reserves is a crucial activity for non-life insurance companies. It involves adjusting the expected evolution of claims over different periods of active policies and their fluctuations. The chain-ladder (CL) technique is recognized as one of the most effective methods for calculating claim reserves in this context. It has become a benchmark within the insurance sector for predicting loss reserves and has been adapted to estimate variability margins. This variability has been addressed through both stochastic and possibilistic analyses. This study adopts the latter approach, proposing the use of the CL framework combined with intuitionistic fuzzy numbers (IFNs). While modeling with fuzzy numbers (FNs) introduces only epistemic uncertainty, employing IFNs allows for the representation of bipolar data regarding the feasible and infeasible values of loss reserves. In short, this paper presents an extension of the chain-ladder technique that estimates the parameters governing claim development through intuitionistic fuzzy regression, such as symmetric triangular IFNs. Additionally, it compares the results obtained with this method with those derived from the stochastic chain ladder by England and Verrall.

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“…These point prediction methods have been applied in the field of temperature prediction, including back-propagation neural network [19,20], artificial neural network [21], gray model [22], genetic algorithm [23,24], and support vector machine [25,26]. However, point prediction only provides one prediction result at each target point, which lacks uncertainty estimation [27,28]. For concrete temperature data in the construction period, due to the existence of data noise in monitored temperature data, the complex and changeable external factors, as well as the subjective uncertainty of sample selection, the point prediction method experiences difficulty in quantifying the uncertainties of the concrete temperature prediction values.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Construction Simulation Coupling a Concrete Temperature Field Interval Prediction Model with Optimized Hybrid-Kernel RVM for Arch Dams

et al. 2020

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Joint grouting simulation is an important aspect of arch dam construction simulation. However, the current construction simulation model simplifies the temperature factors in joint grouting simulation, which leads to the difference between the simulation results and the actual construction schedule. Furthermore, the majority of existing temperature prediction research is based on deterministic point predictions, which cannot quantify the uncertainties of the prediction values. Thus, this study presents a real-time construction simulation method coupling a concrete temperature field interval prediction model to address these problems. First, a real-time construction simulation model is established. Secondly, this paper proposes a concrete temperature interval prediction method based on the hybrid-kernel relevance vector machine (HK-RVM) with the improved grasshopper optimization algorithm (IGOA). The hybrid-kernel method is adopted to ensure the prediction accuracy and generalization ability of the model. Additionally, the improved grasshopper optimization algorithm (IGOA), which utilizes the tent chaotic map and cosine adaptive method to improve the algorithm performance, is developed for the parameter optimization of HK-RVM. Thirdly, concept drift detection based on variable window technology is proposed to update the prediction model. Finally, an arch dam project in China is used as a case study, by which the superiority and applicability of the proposed method are proven.

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Fuzzy-statistical prediction intervals from crisp regression models

Cited by 9 publications

References 20 publications

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

Real-Time Construction Simulation Coupling a Concrete Temperature Field Interval Prediction Model with Optimized Hybrid-Kernel RVM for Arch Dams

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