The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept probability, must deal with fact even in very ordinary circumstances at least some probability values may be imprecise, and questions fail have numerically precise answers.

The effect of perturbations of parameters for uniquely convergent imprecise Markov chains is studied. We provide the maximal distance between the distributions of original and perturbed chain and maximal degree of imprecision, given the imprecision of the initial distribution. The bounds on the errors and degrees of imprecision are found for the distributions at finite time steps, and for the s...

One criterion recommended (1,2) for establishing the maximal allowable imprecision is derived from the biological variability data. According to this criterion, the metrological coefficient of variation must be equal to or less than one-half of the within-subject biological coefficient of variation. When information about biological variability is not available, or when current procedures give ...

–The performance of a radar detector may become inaccurate when key parameters of the system are imprecise. Imprecise parameters are modeled here as fuzzy numbers. The Fuzzy Integrator detector is constructed for a Rician target in Rayleigh background. Results indicate that the precision of the detection performance decreases as parameter imprecision increases. The false alarm rate is particula...

A method for representing and manipulating imprecise and vague information in engineering design is described. Designers and customers preferences are captured with Fuzzy sets. Formal methods for including noise, trade-o strategies and design iteration are included. Introduction Imprecision and vagueness are intrinsic aspects of engineering design. If (at the start of a design process) a propos...

We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.

Imprecision is a long-standing problem in CAD design and high accuracy image-based reconstruction applications. The visual hull which is the closed silhouette equivalent shape of the objects of interest is an important concept in image-based reconstruction. We extend the domain-theoretic framework, which is a robust and imprecision capturing geometric model, to analyze the imprecision in the ou...

In the geodetic applications of the Global Positioning System (GPS) various types of data uncertainty are relevant. The most prominent ones are random variability (stochasticity) and imprecision. Stochasticity is caused by uncontrollable effects during the observation process. Imprecision is due to remaining systematic deviations between data and model due to imperfect knowledge or just for pra...

This paper is an initial exploration of representation, uncertain precision, and dependency as a connected concern that is not easily decomposed. Often for reasons of computational simplicity, the assumption is made that attributes are independent of each other. Similarly, whether dependency exists is classically expressed in terms of first order logic The actuality is that often the assumption...