Data envelopment analysis (DEA) is a method for measuring the relative efficiencies of a set of decision-making units (DMUs) that use multiple inputs to produce multiple outputs. In this paper, we study the measurement of DMU performances in DEA in situations where input and/or output values are given as imprecise data. By imprecise data we mean situations where we only know that the actual val...

INTERVAL ANALYSIS: UNCON-STRAINED AND CONSTRAINED OPTIMIZATION Introduction. Interval algorithms for constrained and un-constrained optimization are based on adaptive, exhaustive search of the domain. Their overall structure is virtually identical to Lipschitz optimization as in [4], since interval evaluations of an objective function φ over an interval vector x correspond to estimation of the ...

Inter-block backtracking (IBB) computes all the solutions of sparse systems of non-linear equations over the reals. This algorithm, introduced in 1998 by Bliek et al., handles a system of equations previously decomposed into a set of (small) k×k sub-systems, called blocks. Partial solutions are computed in the different blocks and combined together to obtain the set of global solutions. When so...

A new clustering strategy is proposed based on interval sets, which is an alternative formulation different from the ones used in the existing studies. Instead of using a single set as the representation of a cluster, each cluster is represented by an interval set that is defined by a pair of sets called the lower and upper bounds. Elements in the lower bound are typical elements of the cluster...

Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of ‘Idempotent Mathematics’ with an emphasis on matrix theory, interval analysis over idempotent semirings is developed. The theory is applied to construction of exact interval solutions to the interval discrete stationa...

Control of real industrial processes is almost always burden with an uncertainty. The reasons of that unfavorable fact are mainly an imprecise modelling and measuring or an influence of some external conditions. A convenient tool for dealing with such class of issues represents the application of models with parametric uncertainty. The mathematical model is then supposed to contain parameters w...

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic. We relax the problem so that if the verification process cannot succeed at the prescribed precision, it outputs an inconclusive result. The problem is solved ...

One feature of contemporary datasets is that instead of the single point value in the p-dimensional space R seen in classical data, the data may take interval values thus producing hypercubes in R . This paper studies the vertices principal components methodology for interval-valued data; and provides enhancements to allow for so-called ‘trivial’ intervals, and generalized weight functions. It ...

Motivation Despite the potential usefulness, the association analysis of gene expression with interval times of two events has been hampered because the occurrence of events can be censored and the conventional survival analysis is not suitable to handle two censored events. However, the recent advances of multivariate survival analysis considering multiple censored events together provide an u...

Statistical units described by interval-valued variables represent a special case of Symbolic Objects, where all descriptors are quantitative variables. In this context, the paper presents two different metrics in R for interval-valued data that are based on the definition of the Hausdorff distance in R. Hausdorff distance in R (for any p ≥ 1) is a L∞ norm between pairs of closed sets. However,...