The practice of stochastic sensitivity analysis described in the decision analysis literature is a testimonial to the need for considering deviations from precise point estimates of ·uncertainty. We propose the use of Bayesian fuzzy probabilities within an influence diagram computational scheme for performing sensitivity analysis during the solution of probabilistic inference and decision probl...

In the paper we consider non-Archimedean fuzziness and probabilities. The idea of non-Archimedean multiple-validities is that (1) the set of values for the vagueness and probability is uncountable infinite and (2) this set is not wellordered. For the first time the non-Archimedean logical multiple-validity was proposed in [13], [14]. We propose non-Archimedean fuzziness that is defined on an in...

Indefinite probabilities are a novel technique for quantifying uncertainty, which were created as part of the PLN (Probabilistic Logic Networks) logical inference engine, which is a key component of the Novamente Cognition Engine (NCE), an integrative AGI system. Previous papers have discussed the use of indefinite probabilities in the context of a variety of logical inference rules, but have o...

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master equation of the asymmetric diffusion process. The annihilation process is also added. The Bethe ansatz solution and the exact N-particle conditional probabilitie...

Three-valued accounts of conditionals frequently promise (a) to conform to the probabilistic view that conditionals are evaluated by conditional probabilities, and (b) to yield a plausible account of compounds of conditionals. However, McGee (1981) shows that probabilistic validity, the conception of validity most naturally associated with the probabilistic view, cannot be characterized by a fi...

Similarity or likelihood normalization techniques are important for speaker veri"cation systems as they help to alleviate the variations in the speech signals. In the conventional normalization, the a priori probabilities of the cohort speakers are assumed to be equal. From this standpoint, we apply the theory of fuzzy measure and fuzzy integral to combine the likelihood values of the cohort sp...

| Uncertainty is present in virtually all replacement decisions due to unknown future events, such as revenue streams, maintenance costs, and in°ation. Fuzzy sets provide a mathematical framework for explicitly incorporating imprecision into the decision making model, especially when the system involves human subjectivity. This paper illustrates the use of fuzzy sets and possibility theory to e...

The deduction problem we will consider can be loosely described as follows: given the probabilities of some events, we wish to compute the probabilities of some other events. The terms "event" and "probability" are to be understood as having the meaning assigned to them in statistics. Probabilistic inference rules have been shown to constitute a key ingredient of expert systems. This report add...

This paper deals with the concept of the “size” or “extent” of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantiti...

Over the past two decades a number of different approaches to “fuzzy probabilities” have been presented. The use of the same term masks fundamental differences. This paper surveys these different theories, contrasting and relating them to one another. Problems with these existing approaches are noted and a theory of “linguistic probabilities” is developed, which seeks to retain the underlying i...