Environmental risk assessment is an essential element in any decision-making process in order to minimize the effects of human activities on the environment. Unfortunately, often environmental data tends to be vague and imprecise, so uncertainty is associated with any study related with these kind of data. Essentially, uncertainty in risk assessment may have two origins – randomness and incompl...

The problem of converting possibility measures into probability measures has received attention in the past, but not by so many scholars. This question is philosophically interesting as part of the debate between probability and fuzzy sets. The imbedding of fuzzy sets into random set theory as done by Goodman and Nguyen (1985), Wang Peizhuang (1983), among others, has solved this question in pr...

We show that analogously to classical probability theory the conditional expectation E ( ? ~ X ) of a fuzzy random variable Y w.r.t. a fuzzy random variable X is w.r.t. a suitable metric the best approximation o f ? by measurable functions ofX. Furthermore, several linear regression functions, i.e. best approximation of ? by linear functions o f z and examples for random LR-fuzzy numbers and Ga...

Recently, two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications were introduced by Grzegorzewski [6, 7, 9]. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this paper we generalize these two classes and propose a new kind of construction methods for fuzzy implications which are ba...

Monte Carlo simulation (MCS) has been widely used for the uncertainty propagations of building simulation tools. In general, most unknown inputs for the MCS are regarded as single probability distributions based on experts’ subjective judgements and assumptions, when simulation information and measured data are inaccurate and insufficient. However, this can lead to meaningless and untrustworthy...

In the literature, a number of fuzzy-based power control schemes have been proposed for systems with a single rate. However, emerging CDMA cellular systems are expected to include multimedia services. In such systems, different services have different quality of service (QoS) requirements, such as minimum transmission rates and tolerable delays. This paper introduces an adaptive fuzzy-based con...

The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutual information of fuzzy partitions and for Kullback-Leibler divergence with respect to fuzzy P-measures are established. In addition, a convexity o...

Information fusion introduces special operators ◦ in probability theory and fuzzy theory. Some serious data certify in each cases these two quite distinct techniques. This communication will show that four postulates are the unique aim of these two theories. Evidence theory and fuzzy set theory replace often probabilities in medicine, economy and control. Fuzzy theory is used for example in Jap...

In the article the possibility of applying one of the methods of data mining – fuzzy association rules to model fuzzy systems is presented. The algorithm of automatic extracting knowledge base is a modification of the Apriori algorithm. The obtained rules of the model contain weights, that are calculated on the basis of measures of fuzzy association rules and constitute probability of fuzzy eve...