97 research outputs found
Pawlak, Belnap and the magical number seven
We are considering the algebraic structure of the Pawlak-Brouwer-Zadeh
lattice to distinguish vagueness due to imprecision from ambiguity due to
coarseness. We show that a general class of many-valued logics useful for
reasoning about data emerges from this context. All these logics can be
obtained from a very general seven-valued logic which, interestingly enough,
corresponds to a reasoning system developed by Jaina philosophers four
centuries BC. In particular, we show how the celebrated Belnap four-valued
logic can be obtained from the very general seven-valued logic based on the
Pawlak-Brouwer-Zadeh lattice
06501 Abstracts Collection -- Practical Approaches to Multi-Objective Optimization
From 10.12.06 to 15.12.06, the Dagstuhl Seminar 06501 ``Practical Approaches to Multi-Objective Optimization\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Robust ordinal regression for value functions handling interacting criteria
International audienceWe present a new method called UTAGMSâINT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTAGMSâINT is a general additive value function augmented by two types of components corresponding to ââbonusââ or ââpenaltyââ values for positively or negatively interacting pairs of criteria, respectively. When calculating value of a particular alternative, a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria. Similarly, a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria. The preference information elicited by the DM is composed of pairwise comparisons of some reference alternatives, as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference, either comprehensively or on a particular criterion. In UTAGMSâINT, ROR starts with identification of pairs of interacting criteria for given preference information by solving a mixed-integer linear program. Once the interacting pairs are validated by the DM, ROR continues calculations with the whole set of compatible value functions handling the interacting criteria, to get necessary and possible preference relations in the considered set of alternatives. A single representative value function can be calculated to attribute specific scores to alternatives. It also gives values to bonuses and penalties. UTAGMSâINT handles quite general interactions among criteria and provides an interesting alternative to the Choquet integral
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
Preference Learning
This report documents the program and the outcomes of Dagstuhl Seminar 14101 âPreference Learningâ. Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies
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