a new approach to define the similarity measure betweeninterval-valued fuzzy sets is presented. the proposed approach isbased on a weighted measure in which the normalized similaritiesbetween lower functions and also between upper functions arecombined by a weight parameter. the properties of this similaritymeasure are investigated. it is shown that, the proposed measurehas some advantages in c...

Real world applications often require dealing with the situations in which the exact numerical values of the (sub)measure of a set may not be provided, but at least some probabilistic assignment still could be done. Also, several concepts in uncertainty processing are linked to the processing of distribution functions. In the framework of generalized measure theory we introduce the probabilisti...

This paper uses a constraint set approach to linear programming problems with equality constraints whose coefficients and/or right-hand side values could be uncertain. We consider three types of uncertainty: probabilistic, fuzzy/possibilistic, and interval. The constraint set generated by the linear constraints under uncertainty is illdefined and difficult to generate. Our approach computes an ...

We define and compare several probabilistic notions of computability for mappings from represented spaces (that are equipped with a measure or outer measure) into computable metric spaces. We thereby generalize definitions by [Ko 1991] and Parker (see [Parker 2003, Parker 2005, Parker 2006]), and furthermore introduce the new notion of computability in the mean. Some results employ a notion of ...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstra...

Abstract. Several concepts of approximate reasoning in uncertainty processing are linked to the processing of distribution functions. In this paper we make use of probabilistic framework of approximate reasoning by proposing a Lebesgue-type approach to integration of non-negative real-valued functions with respect to probabilisticvalued decomposable (sub)measures. Basic properties of the corres...