DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality

Kadziński, Miłosz; Słowiński, Roman

doi:10.1007/s10898-012-9945-9

Cited by 37 publications

(14 citation statements)

References 23 publications

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“…In the following subsections, we discuss preference modeling for two types of indirect preference information that may be considered apart from the classification examples. These are desired class cardinalities [23] and assignment-based pairwise comparisons [20]. The respective constraints are added to E univocal assignment so that they are respected when constructing a univocal recommendation.…”

Section: Construction Of a Univocal Recommendationmentioning

confidence: 99%

“…Desired class cardinalities consist of the minimal N min h,DM and/or maximal N max h,DM number of acts that can be assigned to class Cl h , h ∈ H, with N min h,DM ≤ N max h,DM [23]. Obviously, these requirements may refer to the proportions of the set of acts (e.g., 10%, 25%, or 50%) instead of explicit numbers.…”

Section: Desired Class Cardinalitiesmentioning

confidence: 99%

“…These are desired class cardinalities and assignment-based pairwise comparisons. The former specify the minimal and/or maximal number of acts that can be assigned to each act [23], while the latter indicate imprecise comparison between desired classes for pair of acts, but without specifying any concrete classes [20]. Note that the proposed procedure is more general, being independent of the method used for robustness analysis.…”

Section: Introductionmentioning

confidence: 99%

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Robustness analysis for decision under uncertainty with rule-based preference model

Kadziński

Słowiński

Greco

2016

Information Sciences

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We consider decision under uncertainty as a multi-attribute classification problem where a set of acts is described by outcomes gained with given probabilities. The Decision Maker (DM) provides desired classification for a small subset of reference acts. Such preference information is structured using Dominance-based Rough Set Approach (DRSA), and the resulting lower approximations of the quality class unions are used as an input for construction of an aggregated preference model. We induce all minimal-cover sets of rules being compatible with the non-ambiguous assignment examples, and satisfying some additional requirements that may be imposed by the DM. Applying such compatible instances of the preference model on a set of all acts, we draw conclusions about the certainty of recommendation assured by different minimal-cover sets of rules. In particular, we analyze the diversity of class assignments, assignment-based preference relations, and class cardinalities. Then, we solve an optimization problem to get a univocal (precise) classification for all acts, taking into account the robustness concern. This optimization problem admits incorporation of additional indirect and imprecise preferences in form of desired class cardinalities and assignment-based pairwise comparisons. Finally, we extend the proposed approach to group decision under uncertainty. We present a set of indicators and outcomes for judging the spaces of consensus and disagreement between the DMs.

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Section: Construction Of a Univocal Recommendationmentioning

confidence: 99%

Section: Desired Class Cardinalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robustness analysis for decision under uncertainty with rule-based preference model

Kadziński

Słowiński

Greco

2016

Information Sciences

Self Cite

View full text Add to dashboard Cite

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“…In particular, one may elicit holistic judgments, such as pairwise comparisons of alternatives or criteria (see, e.g., [12,29]), assignment-based pairwise comparisons [19], assignment examples (see, e.g., [9,33]), rank-related requirements [22], or desired class-cardinalities (see, e.g., [23,42]). Furthermore, one may also specify some imprecise statements, like lower and upper bounds for comprehensive scores (see, e.g., [40]) or preference ratios (see, e.g., [28]).…”

Section: Indirect and Imprecise Preference Informationmentioning

confidence: 99%

Post factum analysis for robust multiple criteria ranking and sorting

et al. 2015

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Providing partial preference information for multiple criteria ranking or sorting problems results in the indetermination of the preference model. Investigating the influence of this indetermination on the suggested recommendation, we may obtain the necessary, possible and extreme results confirmed by, respectively, all, at least one, or the most and least advantageous preference model instances compatible with the input preference information. We propose a framework for answering questions regarding stability of these results. In particular, we are investigating the minimal improvement that warrants feasibility of some currently impossible outcome as well as the maximal deterioration by which some already attainable result still holds. Taking into account the setting of multiple criteria ranking and sorting problems, we consider such questions in view of pairwise preference relations, or attaining some rank, or assignment. The improvement or deterioration of the sort of an alternative is quantified with the change of its performances on particular criteria and/or its comprehensive score. The proposed framework is useful in terms of design, planning, formulating the guidelines, or defining the future performance targets. It is also important for robustness concern because it finds which parts of the recommendation are robust or sensitive with respect to the modification of the alternatives' performance values or scores. Application of the proposed approach is demonstrated on the problem of assessing environmental impact of main European cities.

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“…A large number of real-world case studies of multicriteria classification problems in different domains are reported in the literature (e.g., [40] [70]). In practice, these decision problems often imply several decision makers having conflicting objectives and judgements.…”

Section: Introductionmentioning

confidence: 99%