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...

Representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. Fo-cusing on discounted cash flow analysis numerical results are presented, comparisons are made between alter-native modeling methods, and characteristics of the methods are discussed.

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...

There is a well-known interpretation of fuzzy interval in the framework of the theory of imprecise probabilities [1, 2]. To get this, we associate with any fuzzy interval a possibility or necessity measure, and then consider that values of the pointed measures give us lower or upper assessments of probabilities. This interpretation was discussed in detail in [3], and there it is proposed to use...

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...

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...

In recent times, intuitionistic fuzzy sets introduced by Atanassov has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the concept of divergence between intuitionistic fuzzy sets is important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern reco...