Sequential incorporation of imprecise information in multiple criteria decision processes

Mármol, Amparo M.; Puerto, Justo; Fernández, Francisco R.

doi:10.1016/s0377-2217(01)00082-0

Cited by 54 publications

(13 citation statements)

References 20 publications

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“…For the continuous case, see for instance, Weber (1987), Carrizosa et al (1995), Mármol et al (2002). There is also a relevant stream of literature dealing with decision problems with a finite number of alternatives in the context of partial information, both for multi-attribute problems with a single decision maker and for group decision making (see for instance, Kim et al 1999;Ahn et al 2000;Salo 1995;Salo and Hämäläinen 2001;Clímaco and Dias 2006;Contreras and Mármol 2007).…”

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confidence: 99%

Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Hinojosa

Mármol

2009

Group Decis Negot

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Egalitarianism and utilitarianism can be viewed as two opposed axiomatic principles from where to begin the search of appropriate solutions to multi-criteria problems. When a vector of criterion weights is provided, these two principles yield respectively to weighted maxmin solutions, and to weighted utilitarian solutions. However, if only partial information about the importance of the criteria is available, the situation becomes more complex and a variety of solutions which extend the utilitarian and the maxmin solution arise. In this paper we explore some of these solutions and their axiomatic properties. If a utilitarian principle is first considered and a pessimistic or an optimistic rule applied afterwards, then two new solution concepts arise. Utilitarian solutions based on the pessimistic rule are inequality averse, and therefore can be viewed as a compromise between the egalitarian and utilitarian solutions. We also explore the solutions obtained when an egalitarian principle with respect to the criteria is considered and a pessimistic or an optimistic rule is applied to select criterion weights.

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confidence: 99%

Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Hinojosa

Mármol

2009

Group Decis Negot

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“…It is possible to apply this methodology in each step of the process of obtaining leximin solutions. In particular, the sequential procedure proposed in Mármol, Puerto, and Fernández (2002) is specially well-fitted to direct the search for a final consensus solution corresponding to the information provided by the agents.…”

Section: Proof the Results Follows From Lemma 42mentioning

confidence: 99%

Generalized Maximin Solutions in Multicriteria Bargaining

Hinojosa

Mármol

2005

Ann Oper Res

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In this paper we address bargaining games where the agents have to take into account different criteria to value the decisions. We propose the class of generalized maximin solutions, as the natural extension for these games of the maximin solutions in conventional bargaining. In order to refine this solution concept, we define a multicriteria lexicographic partial ordering and present the class of generalized leximin solutions as those that are nondominated with respect to this relation. We establish some properties of these solutions and characterize them as solutions of multicriteria problems.

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“…Other approaches to find the extreme points of S W have also been presented (Carrizosa et al, 1995;Mármol et al, 1998;Puerto et al, 2000;Mármol et al, 2002;Ahn, 2015).…”

Section: Ranking Candidates With Constraints On Rank Position Importancementioning

confidence: 99%

Aggregation of ranked votes considering different relative gaps between rank positions

Ahn

2017

Journal of the Operational Research Society

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This paper considers ranked voting systems to determine the rank order of candidates who compete for a limited number of positions. We show that the preferential voting problems based on the data envelopment analysis (DEA) (Wang et al, 2007) can be solved using the extreme points of constraints on rank position importance incorporated in the formulation. This is basically due to the fact that the so-called inverse positive property of the constraints makes it possible to easily find their extreme points. Further, we emphasize that this finding is not restricted to Wang et al's two linear models, but is also applicable to other DEA-based preferential voting problems, which include the constraints accounting for different relative gaps between rank positions.

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Sequential incorporation of imprecise information in multiple criteria decision processes

Cited by 54 publications

References 20 publications

Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Generalized Maximin Solutions in Multicriteria Bargaining

Aggregation of ranked votes considering different relative gaps between rank positions

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