A general way of representing incomplete information is to use closed and convex sets of probability distributions, which are also called credal sets. Each credal set is associated with uncertainty, whose amount is quantified by an appropriate uncertainty measure. One of the requisite properties of uncertainty measures is the property of additivity, which is associated with the concept of indep...

The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the char...

We propose semantic distance measures based on the criterion of approximate discernibility and on evidence combination. In the presence of incomplete knowledge, the distance measures the degree of belief in the discernibility of two individuals by combining estimates of basic probability masses related to a set of discriminating features. We also suggest ways to extend this distance for compari...

The main statistics used in rough set data analysis, the approximation quality, is of limited value when there is a choice of competing models for predicting a decision variable. In keeping within the rough set philosophy of non–invasive data analysis, we present three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle. Our ma...

This paper considers a plethora of time-series measures of uncertainty for inflation and real output growth, which are widely used in empirical studies. Their relative performances are compared to a benchmark measure using the uncertainty measure reported by individual forecasters in the Survey of Professional Forecasters (SPF) for the period 1982-2008. The results show that the use of real-tim...

The first section gives the measure of uncertainty given by Shannon (1948) and the generalizations thereof by Schvitzenberger (1954), Kullback (1959), Renyi (1961,1965), Kapur (1967, 1968), and Rathie (1970). It gives some postulates characterizing Shannon's entropy, Renyi's entropy of order a and our entropy of order a and type P. It also gives some properties of this most general type of entr...

In portfolio selection models, uncertainty plays an important role. The parameter’s uncertainty leads to getting away from optimal solution so it is needed to consider that in models. In this paper we presented a two-stage robust model that in first stage determines the desired percentage of investment in each industrial group by using return and risk measures from different industries. One rea...