We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions i...

Consider both the classical and some more general invariant decision problems of estimating a continuous distribution function, with the loss function L ( F , a ) = f ( F ( t ) a(t))2h(F(t))dF(t) and a sample of size n from F. It is proved that any nonrandomized estimator can be approximated in Lebesgue measure by the more general invariant estimators. Some methods for investigating the finite ...

The calculation of compatibility measures is an important technique employed in group decision-making with interval multiplicative preference relations. In this paper, a new compatibility measure called the continuous logarithm compatibility, which considers risk attitudes in decision-making based on the continuous ordered weighted geometric averaging (COWGA) operator, is introduced. We also de...

In this paper, we introduce a new sampling plan based on the defective proportion of batch. The proposed sampling plan is based on the distribution function of the proportion defective. A continuous loss function is used to quantify deviations between the proportion defective and its acceptance quality level (AQL).  For practical purpose, a sensitivity analysis is carried out on the different v...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

in this paper, we focus on the study of shearlet transform which isdened by using the hyperbolic functions. as a result we check an admissibilitycondition such that implies the reconstruction formula. to this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.