The problem is sequence prediction in the following setting. A sequence x1, . . . , xn, . . . of discrete-valued observations is generated according to some unknown probabilistic law (measure) μ. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure μ belongs to an arbitrary class C of stochastic processes. We are interested in p...

Uncertainty measures can supply new points of view for analyzing data and help us to disclose the substantive characteristics of data sets. Some uncertainty measures for single-valued information systems or single-valued decision systems have been developed. However, there are few studies on the uncertainty measurement for interval-valued information systems or interval-valued decision systems....

This paper addresses an important issue about the compact representation of the conditional probability distribution (CPD) applied in the well known Bayesian Networks in uncertain causality representation and probabilistic inference. That is, there is an essential difference between the single-valued cases and the multi-valued cases, while this difference does not exist when the CPD is represen...

We develope a construction of an L-fuzzy valued measure by extending a measure defined on a σ-algebra of crisp sets to an L-fuzzy valued TM-countably additive measure defined on a TMclan of L-fuzzy sets in the case when operations for L-fuzzy sets and L-fuzzy real numbers are based on the minimum t-norm TM. Keywords— L-fuzzy set, L-fuzzy real number, L-fuzzy valued measure.

The generalized fuzzy valued θ-Choquet integrals will be established for the given μ-integrable fuzzy valued functions on a general fuzzy measure space, and the convergence theorems of this kind of fuzzy valued integral are being discussed. Furthermore, the whole of integrals is regarded as a fuzzy valued set function on measurable space, the double-null asymptotic additivity and pseudo-double-...

We describe a mechanism for performing probabilistic reasoning in influence diagrams us­ ing interval rather than point valued probabilities. We derive the procedures for node removal (corresponding to conditional expectation) and arc reversal (corresponding to Bayesian condi­ tioning) in influence diagrams where lower bounds on probabilities are stored at each node. The resulting bounds for th...

In [Fuhr 95], we have proposed probabilistic Datalog (pD) as an inference engine for IR. However, a closer look at pD shows that it handles conditional probabilities only in a rather limited way, since it neither allows for the speci cation of conditional probabilities in rules nor is it able to compute conditional probabilities. Given that probabilistic IR should be interpreted as computing th...

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper we shall introduce the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-...

Measuring consistency of preferences is very important in decision-making. This paper addresses this key issue for interval-valued reciprocal preference relations. Existing studies implement one of two different measures: the “classical” consistency measure, and the “boundary” consistency measure. The classical consistency degree of an interval-valued reciprocal preference relation is determine...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.