926 research outputs found
Class-based Rough Approximation with Dominance Principle
Dominance-based Rough Set Approach (DRSA), as the extension of Pawlak's Rough
Set theory, is effective and fundamentally important in Multiple Criteria
Decision Analysis (MCDA). In previous DRSA models, the definitions of the upper
and lower approximations are preserving the class unions rather than the
singleton class. In this paper, we propose a new Class-based Rough
Approximation with respect to a series of previous DRSA models, including
Classical DRSA model, VC-DRSA model and VP-DRSA model. In addition, the new
class-based reducts are investigated.Comment: Submitted to IEEE-GrC201
Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information
Focusing on stochastic programming (SP) with covariate information, this
paper proposes an empirical risk minimization (ERM) method embedded within a
nonconvex piecewise affine decision rule (PADR), which aims to learn the direct
mapping from features to optimal decisions. We establish the nonasymptotic
consistency result of our PADR-based ERM model for unconstrained problems and
asymptotic consistency result for constrained ones. To solve the nonconvex and
nondifferentiable ERM problem, we develop an enhanced stochastic
majorization-minimization algorithm and establish the asymptotic convergence to
(composite strong) directional stationarity along with complexity analysis. We
show that the proposed PADR-based ERM method applies to a broad class of
nonconvex SP problems with theoretical consistency guarantees and computational
tractability. Our numerical study demonstrates the superior performance of
PADR-based ERM methods compared to state-of-the-art approaches under various
settings, with significantly lower costs, less computation time, and robustness
to feature dimensions and nonlinearity of the underlying dependency
Equivalence Checking of Quantum Finite-State Machines
In this paper, we introduce the model of quantum Mealy machines and study the
equivalence checking and minimisation problems of them. Two efficient
algorithms are developed for checking equivalence of two states in the same
machine and for checking equivalence of two machines. They are applied in
experiments of equivalence checking of quantum circuits. Moreover, it is shown
that the minimisation problem is proved to be in \textbf{PSPACE}
Towards a Reliable Framework of Uncertainty-Based Group Decision Support System
This study proposes a framework of Uncertainty-based Group Decision Support
System (UGDSS). It provides a platform for multiple criteria decision analysis
in six aspects including (1) decision environment, (2) decision problem, (3)
decision group, (4) decision conflict, (5) decision schemes and (6) group
negotiation. Based on multiple artificial intelligent technologies, this
framework provides reliable support for the comprehensive manipulation of
applications and advanced decision approaches through the design of an
integrated multi-agents architecture.Comment: Accepted paper in IEEE-ICDM2010; Print ISBN: 978-1-4244-9244-
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