This paper considers two general 0-1 random fuzzy programming problems based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problems are not well defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goal for the objective function, and considering the maximization of the aspir...

In many basic scheduling models, jobs’ processing times and due-dates are deterministic. Practically, they are as uncertain variables in some more models. Furthermore, in a real situation of decision making, there exists uncertainty that can not be described only by fuzziness but also randomness. The purpose of this paper is to develop a methodology for parallel machines scheduling problem with...

A linear regression model with imprecise response and p real explanatory variables is analyzed. The imprecision of the response variable is functionally described by means of certain kinds of fuzzy sets, the LR fuzzy sets. The LR fuzzy random variables are introduced to model usual random experiments when the characteristic observed on each result can be described with fuzzy numbers of a partic...

In the present paper an approaches to the definition of numerical charac-teristics of fuzzy random variables are analyzed and proposed. Appropriatemethods of its calculation, in particular within the framework of shift-scaled representation are obtained. Principles of decision making in fuzzyrandom environment are formulated. Possibilistic-probabilistic models ofportfolio an...

Statistical Learning Theory is commonly regarded as a sound framework within which we handle a variety of learning problems in presence of small size data samples. It has become a rapidly progressing research area in machine learning. The theory is based on real random samples and as such is not ready to deal with the statistical learning problems involving complex fuzzy random samples, which w...

-In this work we present the methods of creating the knowledge bases by using the theory of fuzzy systems as well as the probability and stochastic processes theory. We show that such knowledge-based systems can be applied in different diagnostic tasks. The structure of the reason-result fuzzy model is predefined by experts at the beginning of the task. The notion of probability of fuzzy events...

In some point estimation problems, we may confront imprecise (fuzzy) concepts. One important case is a situation where all observations are fuzzy rather than crisp. In this paper, using fuzzy set theory, we define a fuzzy-valued random variable, a fuzzy unbiased estimator, a fuzzy exponential family, and then we state and prove a Cramér-Rao lower bound for such fuzzy estimators. Finally, we giv...

In standard regression analysis the relationship between one (response) variable and a set of (explanatory) variables is investigated. In a classical framework the response is affected by probabilistic uncertainty (randomness) and, thus, treated as a random variable. However, the data can also be subjected to other kinds of uncertainty, such as imprecision. A possible way to manage all of these...

In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further influence weights) by random variables. Such extension, followed by the implemented software tool, allows for determining ranges reached by concep...

The variance of a fuzzy random variable plays an important role as a measure of central tendency. Some of the main contributions in this topic are consolidated and discussed in this paper. In case of the hypothesis testing problem, bootstrap techniques (Efron and Tibshirani, 1993) have empirically been shown to be efficient and powerful. Algorithms to apply these techniques in practice and some...