Amparo M. Mármol

Sequential incorporation of imprecise information in multiple criteria decision processes

Abstract In this paper we deal with multicriteria decision processes and develop tools that permit to ease the task of analysing such models. We provide a methodology to sequentially incorporate imprecise preference information which is given by means of general linear relations in the weighting coefficients. The results presented allow us to evaluate the quality of the information supplied and can be used to reduce the number of irrelevant alternatives to be presented to the decision maker (DM). Several examples based on multiple criteria linear programming illustrate the results of the paper.

The use of partial information on weights in multicriteria decision problems

An improved apparatus for winding yarn or thread onto a bobbin to form a yarn package is described which comprises a support assembly for maintaining uniform pressure between the drive roll and yarn package during winding so that a yarn package having greater uniformity is produced. The described apparatus further includes an improved take-up roll having a braking means cooperating with a yarn package or bobbin release means, whereby the yarn package cannot be released from the take-up roll until the take-up roll has ceased rotation. Also described is a doffing mechanism associated with the winder for doffing yarn packages from the take-up roll after they are released by the package release means.

A lexicographical compromise method for multiple criteria group decision problems with imprecise information

Abstract This paper addresses multiple criteria group decision making problems where each group member offers imprecise information on his/her preferences about the criteria. In particular we study the inclusion of this partial information in the decision problem when the individuals’ preferences do not provide a vector of common criteria weights and a compromise preference vector of weights has to be determined as part of the decision process in order to evaluate a finite set of alternatives. We present a method where the compromise is defined by the lexicographical minimization of the maximum disagreement between the value assigned to the alternatives by the group members and the evaluation induced by the compromise weights.

Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game

In this paper we study cooperative games with fuzzy payoffs. The main advantage of the approach presented is the incorporation into the analysis of the problem of ambiguity inherent in many real-world collective decision situations. We propose extensions of core concepts which maintain the fuzzy nature of allocations, and lead to a more satisfactory study of the problem within the fuzzy context. Finally, we illustrate the extended core concepts and the approach to obtain the corresponding allocations through the analysis of assignment games with uncertain profits.

An equitable solution for multicriteria bargaining games

In this paper we study bargaining models where the agents consider several criteria to evaluate the results of the negotiation process. We propose a new solution concept for multicriteria bargaining games based on the distance to a utopian minimum level vector. This solution is a particular case of the class of the generalized leximin solutions and can be characterized as the solution of a finite sequence of minimax programming problems.

Generalized Maximin Solutions in Multicriteria Bargaining

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.

Special cases of the tolerance approach in multiobjective linear programming

Abstract In this paper we deal with sensitivity analysis of the Multiobjective Linear Problem. We enlarge the range of meaningful regions of weights that can be handled easily from the tolerance approach point of view. The regions that we propose are important, because they represent the information that the decision maker is able to offer about the relationships between the importance of the different objectives, in terms of marginal substitution rates. Particularly, the well known interval, order and nonhomogeneous order relations are included. We also present an algorithm which reduces the computational effort, in order to get the maximum tolerance percentage. Several examples are included illustrating the results.

Bargaining over multiple issues with maximin and leximin preferences

Global bargaining problems over a finite number of different issues are formalized as cartesian products of classical bargaining problems. For maximin and leximin bargainers we characterize global bargaining solutions that are efficient and satisfy the requirement that bargaining separately or globally leads to equivalent outcomes. Global solutions in this class are constructed from the family of monotone path solutions for classical bargaining problems.

Core, least core and nucleolus for multiple scenario cooperative games ☆

Multiple scenario cooperative games model situations where the worth of the coalitions is valued in different scenarios simultaneously or under different states of nature. In this paper we analyze solution concepts for this class of games keeping the multidimensional nature of the characteristic function. We obtain extensions of the notions of core, least core and nucleolus, and explore the relationship among these solution concepts.

Nash decomposition for process efficiency in multistage production systems

DEA models in which each DMU is organized internally as a sequence of processes or stages are considered.Nash bargaining theory is used to obtain a decomposition of the overall efficiency in the multistage production system.A explicit formula for the Nash decomposition is obtained.Interpretations of the results are provided. Many production systems consist of a sequence of processes or stages. For these systems, relational network DEA can be used and an overall system efficiency (equal to the efficiency of the different processes) can be computed. However, there can be alternative solutions that give different estimations of the process efficiencies and therefore lead to different decompositions of the overall system efficiency. It is not obvious which efficiency decomposition to use. In this paper, it is shown how a Nash bargaining game can be used to compute point estimates of the efficiency of the processes for multistage systems. The proposed approach extends and improves over existing approaches for production systems with just two stages. The rationality principles behind the proposed solution approach are presented and an interesting interpretation of the resulting efficiency decomposition is provided. The fact that this rigorous solution approach leads to such a simple and elegant efficiency decomposition should facilitate its adoption by Expert and Intelligent Systems practitioners.