In [9] we introduced a new framework for asymptotic probabilities. in which a r i-add~t~ve measure is defined on the sample space of all sequences A =< dl.d?. . d, > of finite models. where the uniberse of sf,, is { I . 2. ...n ) . In this framework we Investigated the strong 0-1 law for sentences. whlch states that each sentence either holds in d,, eventually almost surely or fails In d,, even...

In this paper, we are trying to examine trade offs between fuzzy logic and certain Bayesian networks and we propose to combine their respective advantages into fuzzy certain Bayesian networks (FCBN), a certain Bayesian networks of fuzzy random variables. This paper deals with different definitions and classifications of uncertainty, sources of uncertainty, and theories and methodologies present...

The aim of this paper is to extend the classical problem of confidence interval estimation for the mean of a random variable to the case of a fuzzy random variable. The key idea consists in considering a confidence region defined as a ball w.r.t. a given metric, which is centered in the sample mean and whose radius is determined via bootstrapping. The developed approach is illustrated both by m...

In this research we concentrate on developing a bifuzzy model for a Single-period inventory problem. The conventional studies have focused on the cases that the demands are probabilistic and follow certain distribution function; or the demands are considered as fuzzy variables; or the demands is expressed by random fuzzy variable. Recently, fuzzy random variables have been applied to some decis...

This paper considers a fuzzy programming approach for a multi-objective single machine scheduling problem when processing times of jobs are normal random variables. The probabilistic problem is converted into an equivalent deterministic programming problem. Then the fuzzy programming technique has been applied to obtain a compromise solution. A numerical example demonstrates the feasibility of ...

This paper surveys some of the recent results that have been obtained in fuzzy quantum probability theory. In this theory fuzzy events are represented by quantum effects and fuzzy random variables are represented by quantum measurements. Probabilities, conditional probabilities and sequential products of effects are discussed. The relationship between the law of total probability and compatibil...

The present paper is devoted to the transition from crisp domains of probability to fuzzy domains of probability. First, we start with a simple transportation problem and present its solution. The solution has a probabilistic interpretation and it illustrates the transition from classical random variables to fuzzy random variables in the sense of Gudder and Bugajski. Second, we analyse the proc...

Reliability based design optimization has received increasing attention for satisfying high requirements on reliability and safety in structure design. However, in practical engineering design, there are both continuous and discrete design variables. Moreover, both aleatory uncertainty and epistemic uncertainty may associate with design variables. This paper proposes the formulation of random/f...

A weighted linear regression model with impercise response and p-real explanatory variables is analyzed. The LR fuzzy random variable is introduced and a metric is suggested for coping with this kind of variables. A least square solution for estimating the parameters of the model is derived. The result are illustrated by the means of some case studies.

In this paper, assuming cooperative behavior of the decision makers, solution methods for decisionmaking problems in hierarchical organizations under fuzzy randomenvironments are considered. To deal with the formulated two-level linear programming problems involving fuzzy random variables, α-level sets of fuzzy random variables are introduced and an α-stochastic two-level linear programming pro...