Pythagorean fuzzy TOPSIS method based on 2-tuple probability weight

In this paper, the concept of 2-tuple probability weight is presented, and on this basis, the technique for order preference by similarity to ideal solution (TOPSIS) method in Pythagorean fuzzy environment is given. First, the definition of 2-tuple probability weight is put forward, and two examples are provided to illustrate that 2-tuple probability weight can effectively prevent the loss of information. Second, the notion of real-value 2-tuple is defined for any two real numbers, and some basic operations, operation properties, and sorting functions are introduced. Finally, a 2-tuple probability weight Euclidean distance is provided, a new Pythagorean fuzzy TOPSIS method is further proposed, and the flexibility and effectiveness of the proposed methods are illustrated by an example and two comparative analyses.

On the Empirical Validity of Cumulative Prospect Theory: Experimental Evidence of Rank‐Independent Probability Weighting

Cumulative Prospect Theory (CPT), the leading behavioral account of decisionmaking under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by assuming that the probability weight applied to a given outcome depends on its ranking. We devise a simple and direct nonparametric method for measuring the change in relative probability weights resulting from a change in payoff ranks. We find no evidence that these weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences imply that the percentage change in probability weights should be an order of magnitude larger than we observe. It follows either that probability weighting is not rank‐dependent, or that the weighting function is nearly linear. Nonparametric measurement of the change in relative probability weights resulting from changes in probabilities rules out the second possibility. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well‐known certainty effect.

Assessing balance in outcome regressions

An outcome regression controlling for observed confounders remains a popular way to assess the causal effect of an exposure in epidemiology, despite more modern causal techniques for adjusting for observed confounders, such as inverse probability weighting. A feature of inverse probability weighting is that checking balance of confounders in the control and exposure groups after confounder adjustment is simple. However, researchers using outcome regressions commonly do not check confounder balance after controlling for confounders. Although outcome regressions will balance any confounder specified in the model, the confounder value the model balances at is not transparent. We show that a matrix representation of an outcome regression reveals that an outcome regression includes a weight similar to an inverse probability weight. We also show that outcome regressions may not be balancing at the sample mean of the confounders particularly if interactions are not included with the exposure, which is typically the case in outcome regressions. Finally, we show that the coefficient of the exposure in an outcome regression is simply the difference between two weighted counterfactuals. Thus, there is an important connection between traditional outcome regression and modern causal techniques.

Market Expectations And Probability Distributions Implicit In Option Prices

This paper investigates whether specific characteristics of the returns distributions implied by options prices constitute useful information for the purpose of predicting changes in market direction. The key distributional characteristics we focus on are skewness, kurtosis, and the probability weight in the extreme tails of the implied distributions. We present a new methodology for extracting the returns distributions and apply it to S&P 500 index futures-options prices for twenty days surrounding the four largest market reversals in calendar 2001.

Fuelbed ignition potential and bark morphology explain the notoriety of the eucalypt messmate 'stringybark' for intense spotting

In south-eastern Australia, bark of the ‘stringybark’ eucalypt group, and notably that of messmate (Eucalyptus obliqua L’Hér.), is notorious for intense spotting and it is likely that firebrands of this type contribute significantly to loss of life and property during major wildfires. The fuelbed ignition potential by glowing samples was laboratory tested on excised sections of Pinus radiata D. Don litterbed at moisture contents between 2 and 8% and for ‘no-wind’ or for ‘wind’ of 1 m s–1. Prepared samples of outer bark between 0.5 and 1.6 g were combusted until they attained ~20% of initial mass before placement. For ‘no-wind’, flaming ignition did not occur and the probability of glowing ignition appeared to depend on the chance of contact with needles. For ‘wind’, the probability of flaming ignition was a function of sample glowing mass and fuelbed moisture content. Its ignition probability, weight-for-weight, appears to exceed that reported for other forest firebrands, including bark of E. globulus Labill. However, it is likely that the notoriety of messmate bark is also due, in part, to its morphology and in-flight behaviour. It is argued that firebrand laboratory tests to date may poorly reflect the ignition potential of similar samples after flight.