This paper provides the measure theoretic basis for a theory of possibilistic processes. We generalize the definition of a product τ field to an indexed family of τ -fields, without imposing an ordering on the index set. We also introduce the notion ‘measurable cylinder’ and show that any product τ -field can be generated by its associated field of measurable cylinders. Furthermore, we introduc...

This paper considers new downside risk-aversion models for linear optimization (linear programming) with discrete fuzzy random variables. Through new downside risk measures for fuzzy stochastic optimization problems, possibilistic low partial moment (PLPM) models are constructed by incorporating possibility and necessity measures into classical low partial moment. To provide practical models, t...

Possibilistic logic in general [7, 8, 9, 10] investigates how possibilistic uncertainty about propositions is propagated when making inferences in a formal logical system. In this paper, we look at a very particular aspect of possibilistic logic: we investigate how, under certain independence assumptions, the introduction of possibilistic uncertainty in classical propositional logic leads to th...

In this paper, we compare merging operators in possibilistic logic. We first propose an approach to evaluating the discriminating power of a merging operator. After that, we analyze the computational complexity of existing possibilistic merging operators. Finally, we consider the compatibility of possibilistic merging operators with propositional merging operators.

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...

We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negat...

We consider linear equality systems where all the parameters may be fuzzy variables specified by their possibility distribution, the operations addition and multiplication by a real number of fuzzy parameters are defined via a suptriangular norm composition, and the equations are understood in possibilistic sense. We show that when the triangular norm defining the operations and equations is co...

The probabilistic Noisy OR model has been widely used as a means of reducing the amount of probabilistic information that is needed to specify the interaction between groups of variables. Motivated by our work on the diagnosis of faults in satellite subsystems , which required a similar synthesis of partial possibilistic information on interactions , we consider a number of ways of gener-alisin...

Possibilistic logic provides a convenient tool for dealing with inconsistency and handling uncertainty. In this paper, we propose possibilistic description logics (DLs) as an extension of description logics. We give semantics and syntax of possibilistic description logics. Two kinds of inference services are considered in our logics and algorithms are provided for them. These algorithms are imp...

Abstract: This paper deals with a portfolio selection problem with fuzzy return rates. A possibilistic mean VaR model was proposed for portfolio selection. Specially, we present a mathematical programming model with possibilistic constraint. The possibilistic programming problem can be solved by transforming it into a linear programming problem. A numerical example is given to illustrate the be...