A weighted linear regression model with impercise response and p-real explanatory variables is analyzed. The LR fuzzy random variable is introduced and a metric is suggested for coping with this kind of variables. A least square solution for estimating the parameters of the model is derived. The result are illustrated by the means of some case studies.

Abstract Statistical relational learning (SRL) frameworks are effective at defining probabilistic models over complex data. They often use weighted first-order logical rules where the weights of govern interactions and usually learned from Existing weight approaches typically attempt to learn a set that maximizes some function data likelihood; however, this does not always translate optimal per...

In a robust parameter design (RPD) problem, the experimenter is interested to determine the values of con-trol factors such that responses will be robust or insensitive to variability of the noise factors. Response sur-face methodology (RSM) is one of the effective methods that can be employed for this purpose. Since quality of products or processes is usually evaluated through several quality ...

Metric Temporal Logic (MTL) is a generalisation of Linear Temporal Logic in which the Until and Since modalities are annotated with intervals that express metric constraints. In this paper we show that over the reals MTL has the same expressive power as monadic first-order logic with binary order relation < and an infinite collection of unary functions +q, where q is a non-negative rational. Th...

We introduce new classes of weighted automata on words. Equipped with pebbles and a two-way mechanism, they go beyond the class of recognizable formal power series, but capture a weighted version of first-order logic with bounded transitive closure. In contrast to previous work, this logic allows for unrestricted use of universal quantification. Our main result states that pebble weighted autom...