Convolution of fuzzy distributions in decision-making

Kofler, Eduard; Zweifel, Peter

doi:10.1007/bf02925486

Cited by 6 publications

(7 citation statements)

References 2 publications

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“…The probability distribution information expressed by Eq. 2 is defined as linear partial information (LPI) (Kofler and Zweifel 1991), which is a particular type of stochastic partial information (SPI). Therefore, by incorporating Eq.…”

Section: Modeling Formulationmentioning

confidence: 99%

“…. ; p Ã n satisfy n of the restrictions contained in HP B b as independent equations and the restriction P j=1 n p j = 1 must be among these n equations (Kofler and Zweifel 1991). Meanwhile, the expected value E(X) of a random variable X with partial distribution probability expressed as Eq.…”

Section: Modeling Formulationmentioning

confidence: 99%

“…Meanwhile, the expected value E(X) of a random variable X with partial distribution probability expressed as Eq. 2 can be determined within the expected interval [E min (X), E max (X)], where E min (X) = min fp Ã g P n j¼1 p j x j and E max (X) = max fp Ã g P n j¼1 p j x j (Kofler and Zweifel 1991). Therefore, model (3) would reach its lower and upper bounds when the probabilities inflow q j achieve the extreme points determined by (3d) and (3e).…”

Section: Modeling Formulationmentioning

confidence: 99%

“…Step 4 According to the principal proposed by Kofler and Zweifel (1991), the final optimal objective function for model (3) can be obtained…”

Section: Modeling Formulationmentioning

confidence: 99%

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Inexact two-stage stochastic partial programming: application to water resources management under uncertainty

Fan

Huang

Guo

et al. 2011

Stoch Environ Res Risk Assess

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In this study, an inexact two-stage stochastic partial programming (ITSPP) method is developed for tackling uncertainties presented as intervals and partial probability distributions. A scenario-based interactive algorithm is proposed to solve the ITSPP model. This algorithm is implemented through: (i) obtaining extreme points of the linear partial information (LPI); (ii) generating an inexact two-stage stochastic programming (ITSP) model under each extreme point; (iii) solving ITSP models through interactive algorithm proposed by Huang and Loucks (Civil Eng Environ Syst 17: 2000); (iv) acquiring the interval solutions under each extreme point and the final optimal interval for the objective function. The developed method is applied to a case study for waterresources planning. The modelling results can generate a series of decision alternatives under various system conditions, and thus help decision makers identify the desired water-resources management policies under uncertainty.

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Section: Modeling Formulationmentioning

confidence: 99%

Section: Modeling Formulationmentioning

confidence: 99%

Section: Modeling Formulationmentioning

confidence: 99%

“…Step 4 According to the principal proposed by Kofler and Zweifel (1991), the final optimal objective function for model (3) can be obtained…”

Section: Modeling Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Inexact two-stage stochastic partial programming: application to water resources management under uncertainty

Fan

Huang

Guo

et al. 2011

Stoch Environ Res Risk Assess

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“…Kofler and Menges (1977) were able to show that a piece of information regarding probabilities of possible outcomes such as r 1 ≥ r 3 (with r 1 + r 2 + r 3 + ••• r n = 1) can be systematically exploited for decision-making. LPI theory has led to a series of publications, notably by Kofler and Menges (1979), Kofler (1988) and Kofler and Zweifel (1988, 1991, 1993.…”

Section: Introductionmentioning

confidence: 99%

Bridging the gap between risk and uncertainty in insurance

Zweifel¹

2021

Geneva Pap Risk Insur Issues Pract

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This contribution evokes Orio Giarini’s courage to think ‘outside the box’. It proposes a practical way to bridge the gap between risk (where probabilities of occurrence are fully known) and uncertainty (where these probabilities are unknown). However, in the context of insurance, neither extreme applies: the risk type of a newly enrolled customer is not fully known, loss distributions (especially their tails) are difficult to estimate with sufficient precision, the diversification properties of a block of policies acquired from another company can be assessed only to an approximation, and rates of return on investment depend on decisions of central banks that cannot be predicted too well. This contribution revolves around the launch of an innovative insurance product, where the company has a notion of whether a favourable market reception is more likely than an unfavourable one, of the chance of obtaining approval from the regulatory authority and the risk of a competitor launching a similar innovation. Linear partial information theory is proposed and applied as a particular practical way to systematically exploit the imprecise information that may exist for all of these aspects. The decision-making criterion is maxEmin, an intuitive modification of the maximin rule known from games against nature.

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Linear partial information with applications

Kofler

2001

Fuzzy Sets and Systems

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Convolution of fuzzy distributions in decision-making

Cited by 6 publications

References 2 publications

Inexact two-stage stochastic partial programming: application to water resources management under uncertainty

Inexact two-stage stochastic partial programming: application to water resources management under uncertainty

Bridging the gap between risk and uncertainty in insurance

Linear partial information with applications

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