Probability assessments of events are often linguistic in nature. We model them by means of possibilistic probabilities (a version of Zadeh’s fuzzy probabilities with a behavioural interpretation) with a suitable shape for practical implementation (on a computer). Employing the tools of interval analysis and the theory of imprecise probabilities we argue that the verification of coherence for t...

We developed a new decision-making model with probabilistic information and used the concept of the immediate probability to aggregate the information. This type of probability modifies the objective probability by introducing the attitudinal character of the decision maker. In doing so, we use the ordered weighting average (OWA) operator. When using this model, it is assumed that the informati...

The new method for risk assessment of the man-machine system functioning is proposed. The feature of the method is combining the fuzzy fault tree analysis and theory of fuzzy reliability of algorithmic processes. This provides a consideration from a unified framework the structural accidents with algorithms of its detecting and avoiding. Method also allows to use fuzzy “if-then” rules about man...

In this paper, two types of fuzzy probability spaces will be introduced and their applications in methods of decision making under risk (especially in the Decision Matrix Method) will be described. First, a fuzzy probability space that generalizes the classical probability space (<,Bn, p) to the situation of fuzzy random events will be studied. It will be applied to perform fuzzy discretization...

The management of uncertainty and imprecision is becoming more and more important in knowledge-based systems. Fuzzy logic provides a systematic basis for representing and inferring with this kind of knowledge. This paper describes an approach for fuzzy inference based on an uncertainty forward propagation method and a change in the granularity of the elements involved. The proposed model is abl...

This paper gives an algorithm which, given any boolean function F whose n arguments are known probabilities, will deduce the tightest possible upper and lower bounds (assuming nothing is known about the correlations among the probabilities) on the value of F. This may be accomplished by solving a 2 n-dimensional linear program. (It is not suprising that the linear program has exponential dimens...

Exact small-sample methods for discrete data use probability distributions that do not depend on unknown parameters. However, they are conservative inferentially: the actual error probabilities for tests and confidence intervals are bounded above by the nominal level. This article surveys ways of reducing or even eliminating the conservatism. Fuzzy inference is a recent innovation that enables ...

In most applications, probabilities of states of nature in decision making are not known exactly due to a lack of complete information. If the available information is represented by a small number of statistical data, Walley’s imprecise Dirichlet model may be regarded as a tool for determining interval probabilities of states of nature. It turns out that the resulting expected utilities consti...

Part-of-Speech(POS) tagging is a process of assigning a POS to each word in a sentence. Since many words are often ambiguous in their POSs, POS tagging must be able to select the best POS sequence for a given sentence. Recently, probabilis-tic approaches have shown very promising results to solve such ambiguity problems. Probabilistic approaches, however, usually require lots of training data t...

In Savage [41] a 'behavioral foundation' was given for subjective probabilities, to be used in the maximization of expected utility. This paper analogously gives a behavioral foundation for fuzzy measures, to be used in the maximization of 'Choquet-expected utility'. This opens the way to empirical verification or falsification of fuzzy measures, and frees them of their 'ad hoc' character.