Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth values. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we devel...

Fuzziness is discussed in the context of multivalued lo&, and a corresponding view of fuzzy sets is given. Fuzzy random variables are introduced as random variables whose values are not real but fuzzy numbers, and subsequently redefined as a particular kind of fuzzy set. Expectations of fuzzy random variables, characteristic f~cti~ of fuzzy events, probabilities connected to fuzzy random variab...

The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuz...

One of the important challenges in Graphical models is the problem of dealing with the uncertainties in the problem. Among graphical networks, fuzzy cognitive map is only capable of modeling fuzzy uncertainty and the Bayesian network is only capable of modeling probabilistic uncertainty. In many real issues, we are faced with both fuzzy and probabilistic uncertainties. In these cases, the propo...

The unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors. Concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so-called fuzzy relative frequencies for fuzzy data, whereby the fuzzy relative frequency of a set is a fuzzy number. A...

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with hesitant fuzzy information, some new decision analysis are proposed. Then, we have developed some new probability aggregation operators with hesitant fuzzy information: probability hesitant fuzzy weighted average (P-HFWA) operator, immediate probability hesitant ...

Distorted probabilities are an important family of fuzzy measures. In a recent paper we introduced m-dimensional distorted probabilities, which generalize the former and permit us to have a smooth transition from distorted probabilities to unconstrained ones. In this paper we introduce the union condition and the strict union condition, and we show that when these conditions hold for a fuzzy me...

A formal analysis of probabilities, possibilities, and fuzzy sets is presented in this paper. A number of theorems proved show that probabilities carry more information per bit than both possibilities and fuzzy sets. The cost of this higher capacity is increased computational complexity and reduced computational eeciency. The resulting trade-oo of high complexity and information capacity versus...