50,484 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
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Portfolio optimisation models and properties of return distributions
Mean-risk models have been widely used in portfolio optimisation. However, such models may
produce portfolios that are dominated with respect to second order stochastic dominance and therefore not
optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio
which is nondominated with respect to second order stochastic dominance and whose return distribution
has specified desirable properties. The problem is multi-objective and is transformed into a single
objective problem by using the reference point method, in which target levels, known as aspiration points,
are specified for the objective function values. A model is proposed in which the aspiration points relate to
ordered return outcomes of the portfolio return. The model is extended by additionally specifying
reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models
are studied. The performance of the models on real data drawn from the Hang Seng index is also
investigated
Linking objective and subjective modeling in engineering design through arc-elastic dominance
Engineering design in mechanics is a complex activity taking into account both objective modeling processes derived from physical analysis and designers’ subjective reasoning. This paper introduces arc-elastic dominance as a suitable concept for ranking design solutions according to a combination of objective and subjective models. Objective models lead to the aggregation of information derived from physics, economics or eco-environmental analysis into a performance indicator. Subjective models result in a confidence indicator for the solutions’ feasibility. Arc-elastic dominant design solutions achieve an optimal compromise between gain in performance and degradation in confidence. Due to the definition of arc-elasticity, this compromise value is expressive and easy for designers to interpret despite the difference in the nature of the objective and subjective models. From the investigation of arc-elasticity mathematical properties, a filtering algorithm of Pareto-efficient solutions is proposed and illustrated through a design knowledge modeling framework. This framework notably takes into account Harrington’s desirability functions and Derringer’s aggregation method. It is carried out through the re-design of a geothermal air conditioning system
Rough set and rule-based multicriteria decision aiding
The aim of multicriteria decision aiding is to give the decision maker a recommendation concerning a set of objects evaluated from multiple points of view called criteria. Since a rational decision maker acts with respect to his/her value system, in order to recommend the most-preferred decision, one must identify decision maker's preferences. In this paper, we focus on preference discovery from data concerning some past decisions of the decision maker. We consider the preference model in the form of a set of "if..., then..." decision rules discovered from the data by inductive learning. To structure the data prior to induction of rules, we use the Dominance-based Rough Set Approach (DRSA). DRSA is a methodology for reasoning about data, which handles ordinal evaluations of objects on considered criteria and monotonic relationships between these evaluations and the decision. We review applications of DRSA to a large variety of multicriteria decision problems
Sorted-pareto dominance: an extension to pareto dominance and its application in soft constraints
The Pareto dominance relation compares decisions
with each other over multiple aspects, and any decision that
is not dominated by another is called Pareto optimal, which is
a desirable property in decision making. However, the Pareto
dominance relation is not very discerning, and often leads to
a large number of non-dominated or Pareto optimal decisions.
By strengthening the relation, we can narrow down this nondominated
set of decisions to a smaller set, e.g., for presenting
a smaller number of more interesting decisions to a decision
maker. In this paper, we look at a particular strengthening of the
Pareto dominance called Sorted-Pareto dominance, giving some
properties that characterise the relation, and giving a semantics
in the context of decision making under uncertainty. We then
examine the use of the relation in a Soft Constraints setting, and
explore some algorithms for generating Sorted-Pareto optimal
solutions to Soft Constraints problems
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