On possibilistic representations of fuzzy intervals

Stefanini, Luciano; Guerra, María Letizia

doi:10.1016/j.ins.2017.04.004

Cited by 17 publications

(7 citation statements)

References 34 publications

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“…The ACF-representation and its properties are studied in [20] where the relationship between ACF and quantile functions, which we apply to Value at Risk hereafter, is proved and resumed in what follows.…”

Section: Average Cumulative Functionmentioning

confidence: 99%

“…The choice of ACF, introduced in [20] as an alternative representation of fuzzy numbers, is justified in terms of an interesting link which can be established between ACF-representation and quantile functions, without requiring distributional assumptions. In [21] we extend the ACF analysis and in particular we clarify the crucial role of ACF in determining the membership function from experimental data.…”

Section: Introductionmentioning

confidence: 99%

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Value at Risk Based on Fuzzy Numbers

Guerra

Sorini

2020

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Value at Risk (VaR) has become a crucial measure for decision making in risk management over the last thirty years and many estimation methodologies address the finding of the best performing measure at taking into account unremovable uncertainty of real financial markets. One possible and promising way to include uncertainty is to refer to the mathematics of fuzzy numbers and to its rigorous methodologies which offer flexible ways to read and to interpret properties of real data which may arise in many areas. The paper aims to show the effectiveness of two distinguished models to account for uncertainty in VaR computation; initially, following a non parametric approach, we apply the Fuzzy-transform approximation function to smooth data by capturing fundamental patterns before computing VaR. As a second model, we apply the Average Cumulative Function (ACF) to deduce the quantile function at point p as the potential loss VaRp for a fixed time horizon for the 100p% of the values. In both cases a comparison is conducted with respect to the identification of VaR through historical simulation: twelve years of daily S&P500 index returns are considered and a back testing procedure is applied to verify the number of bad VaR forecasting in each methodology. Despite the preliminary nature of the research, we point out that VaR estimation, when modelling uncertainty through fuzzy numbers, outperforms the traditional VaR in the sense that it is the closest to the right amount of capital to allocate in order to cover future losses in normal market conditions.

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Section: Average Cumulative Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Value at Risk Based on Fuzzy Numbers

Guerra

Sorini

2020

Axioms

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“…It is worth emphasising that the linear trapezoidal shape represents the propagation of the epistemic uncertainty, decreasing with the increase of the α-cut from α = 0 up to α = 1. Nevertheless, the hybrid fuzzy -stochastic 1D site response analysis proposed in this paper is not restricted to the above linear membership function but other techniques for generating nonlinear membership functions can be used (see, e.g., Pham and Valliappan, [34], Stefanini et al [35]).…”

Section: Construction Of the Soil Parameter Membership Functionmentioning

confidence: 99%

Hybrid fuzzy – stochastic 1D site response analysis accounting for soil uncertainties

Tombari

Stefanini

2019

Mechanical Systems and Signal Processing

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“…From another point of view, Goetschel and Voxman (1986) proposed an equivalent representation named as L-U representation in accordance with the lower and upper branches, which define the two endpoints of an α-cut. Stefanini and Guerra (2017) suggested ACF-representation to describe a fuzzy interval by using a new defined average cumulative function on the basis of the possibility theory. It should be mentioned that the typical L-R representation in Dubois and Prade (1988) is utilized to delineate fuzzy interval in this paper, and the corresponding fuzzy interval is termed as LR-FI accordingly.…”

Section: Introductionmentioning

confidence: 99%

An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

Zhao

Han

Zhou

2021

Preprint

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The operational law put forward by Zhou et al. on strictly monotone functions with regard to regular LR fuzzy numbers makes a valuable push to the development of fuzzy set theory. However, its applicable conditions are confined to strictly monotone functions and regular LR fuzzy numbers, which restricts its application in practice to a certain degree. In this paper, we propose an extensive operational law that generalizes the one proposed by Zhou et al. to apply to monotone (but not necessarily strictly monotone) functions with regard to regular LR fuzzy intervals (LR-FIs), of which regular fuzzy numbers can be regarded as particular cases. By means of the extensive operational law, the inverse credibility distributions (ICDs) of monotone functions regarding regular LR-FIs can be calculated efficiently and effectively. Moreover, the extensive operational law has a wider range of applications, which can deal with the situations hard to be handled by the original operational law. Subsequently, based on the extensive operational law, the computational formulae for expected values (EVs) of LR-FIs and monotone functions with regard to regular LR-FIs are presented. Furthermore, the proposed operational law is also applied to dispose fuzzy optimization problems with regular LR-FIs, for which a solution strategy is provided, where the fuzzy programming is converted to a deterministic equivalent first and then a newly-devised solution algorithm is utilized. Finally, the proposed solution strategy is applied to a purchasing planning problem, whose performances are evaluated by comparing with the traditional fuzzy simulation-based genetic algorithm. Experimental results indicate that our method is much more efficient, yielding high-quality solutions within a short time.

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On possibilistic representations of fuzzy intervals

Cited by 17 publications

References 34 publications

Value at Risk Based on Fuzzy Numbers

Value at Risk Based on Fuzzy Numbers

Hybrid fuzzy – stochastic 1D site response analysis accounting for soil uncertainties

An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

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