Jacinto González-Pachón

Aggregation of partial ordinal rankings: an interval goal programming approach

Abstract This paper shows how interval goal programming can be a useful tool for aggregating incomplete individual patterns of preference in a group decision-making problem. The different consensus solutions obtained have a precise preferential meaning and hold interesting properties. The way in which the methodology functions is illustrated with the help of a numerical example. Scope and purpose This paper deals with group decision-making problems where decision makers are not able to give a complete ranking of alternatives but partial orders. The aggregation of these partial orders is addressed within a distance-based framework. The proposed approach is made operational with the help of an Interval Goal Programming formulation.

Distance-based consensus methods: a goal programming approach

Several authors have proposed a social choice function based upon distance-consensus between different committee rankings. Under this framework, the total absolute disagreement between committees is minimised. The purpose of this paper is to formulate the underlying optimisation problem as a goal programming (GP) model. To do this, the following three GP formulations are proposed: (a) a linear weighting GP model, where consensus is established by the minimisation of the weighted aggregated disagreement, (b) a MINMAX GP model, where the consensus is defined as the minimisation of the maximum disagreement and (c) an extended GP model, which subsumes the two previous formulations as particular cases.

Inferring consensus weights from pairwise comparison matrices without suitable properties

Abstract Pairwise comparison is a popular method for establishing the relative importance of n objects. Its main purpose is to get a set of weights (priority vector) associated with the objects. When the information gathered from the decision maker does not verify some rational properties, it is not easy to search the priority vector. Goal programming is a flexible tool for addressing this type of problem. In this paper, we focus on a group decision-making scenario. Thus, we analyze different methodologies for getting a collective priority vector. The first method is to aggregate general pairwise comparison matrices (i.e., matrices without suitable properties) and then get the priority vector from the consensus matrix. The second method proposes to get the collective priority vector by formulating an optimization problem without determining the consensus pairwise comparison matrix beforehand.

Forest management with multiple criteria and multiple stakeholders: an application to two public forests in Spain.

Abstract Nowadays most forest management problems require the integration of multiple criteria, at the same time as considering the points of view of several stakeholders with different perceptions of predefined criteria. As part of this theoretical orientation, a recent method for aggregating individual preferences expressed through pairwise comparison matrices has been adapted and applied in this paper to elicit social weights in the context of a forest management problem. The method was applied to two public forests in Spain. Four objectives were considered to be relevant in this exercise: biodiversity, net carbon captured, veneer volume and net present value. Twenty-three interviews with graduate students of the forestry school of the Technical University of Madrid were made in a pairwise comparison format. The respective 23 pairwise comparison matrices were aggregated into a final consensus matrix, which aims to represent the social importance attached to the four objectives considered. The applied method allows the establishment of a balance between the majority and minority principles.

A method for dealing with inconsistencies in pairwise comparisons

Abstract The Pairwise Comparison method is a powerful inference tool for assessing the relative importance of a set of items. Formally, its objective is to make compatible decision makers assignments (paired comparison) with properties needed for obtaining an overall rank. In this paper, we propose a distance-based framework for analysing this kind of compatibility. In this context, Goal Programming is proposed as an attractive and flexible tool.

Transitive approximation to pairwise comparison matrices by using interval goal programming

Paired comparison is a very popular method for establishing the relative importance of n objects, when they cannot be directly rated. The challenge faced by the pairwise comparison method stems from some missing properties in its associated matrix. In this paper, we focus on the following general problem: given a non-reciprocal and inconsistent matrix computing intransitivities, what is its associated ranking (defined by importance values)? We propose to use inconsistencies as a source of information for obtaining importance values. For this purpose, a methodology with a decomposition and aggregation phase is proposed. Interval Goal Programming will be a useful tool for implementing the aggregation process defined in the second phase.

Soft dimension theory

Classical dimension theory, when applied to preference modeling, is based upon the assumption that linear ordering is the only elemental notion for rationality. In fact, crisp preferences are in some way decomposed into basic criteria, each one being a linear order. In this paper, we propose that indeed dimension is relative to a previous idea of rationality, but such a rationality is not unique. In particular, we explore alternative approaches to dimension, based upon a more general representation and allowing different classes of orders for basic criteria. In this way, classical dimension theory is generalized. As a first consequence, we explore the existence of crisp preference representations not being based upon linear orders. As a second consequence, it is suggested that an analysis of valued preference relations can be developed in terms of the representations of all α-cuts.

Searching for the dimension of valued preference relations

The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference relations by means of a search for the number of underlying criteria allowing its representation in real space. A general representation theorem for arbitrary crisp binary relations is obtained, showing the difference in representation between incomparability-related to the intersection operator-and other inconsistencies-related to the union operator. A new concept of dimension is therefore proposed, taking into account inconsistencies in source of information. Such a result is then applied to each alpha-cut of valued preference relations

An analytical framework for aggregating multiattribute utility functions

This paper proposes a procedure for aggregating individual cardinal utility functions into a social utility function that represents the preferences of all the individuals as a whole. The procedure is non-interactive and is based upon the determination of the utility consensus values. This is accomplished by minimizing a distance function model that is transformed into an Archimedean goal programming problem. The procedure is applied to a general group multilinear utility function.

Satisficing Logic And Goal Programming: Towards An Axiomatic Link

Abstract This note attempts to elucidate the basic convention or axioms that underpin the Goal Programming approach. By interpreting the meaning of these axioms some links between bounded human rationality theories based upon the Simonian concept of “satisficing” and Goal Programming are established.