Directional instability in the eigenvectors of positive reciprocal matrices

This article addresses the issues of rank stability and ‘bilateral’ consistency that arise when a matrix‐based decision analysis procedure is perceived as capable of yielding more than one weighting vector, for example, both a right and component‐wise inverted left eigenvector. Simple directional constraints that characterize both of the above issues are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Reduction of pairwise comparisons in decision making via a duality approach

Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi‐criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi‐criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one. Copyright © 1999 John Wiley & Sons, Ltd.     

A multi-criterion experimental comparison of three multi-attribute weight measurement methods

The research compared three major multi-attribute weight measurement methods using multiple criteria: theoretical validity, predictive performance, and perceived performance. Major findings include (1) all three methods are theoretically valid using the EAM (Equal Weight Averaging Model) as the standard of comparison, (2) EAM outperforms SMART (Simple Multi-Attribute Rating Technique) and SMART outperforms AHP (Analytical Hierarchy Process) in terms of predictive performance, (3) in terms of perceived performance, EAM is considered more difficult and less preferred than AHP, but has equal trustworthiness. The research has demonstrated how self-estimation methods for multi-attribute analysis can be verified and improved theoretically and empirically by using weights and values from the EAM model as a theoretical validity standard. © 1998 John Wiley & Sons, Ltd.     

Generating consensus priority interval vectors for group decision‐making in the AHP

Many practical and important decision‐making problems are complicated by at least two factors: (1) the qualitative/subjective nature of some criteria often results in uncertainty in the individual ratings; and (2) group decision‐making is involved and some means of aggregating individual ratings is required. Traditionally, both individual and group priorities have been represented as point estimates, but this approach presents severe limitations for accommodating imprecision in the decision‐making process. This paper examines the group decision‐making problem in the context where priorities are represented as numeric intervals. A set of techniques that could be used at some of the phases of an analytic hierarchy process (AHP)‐based group decision‐making process, which has the objective of generating a ‘consensus’ priority that represents the group's opinion with regards to the relative importance of a set of N objects (e.g. criteria, alternatives), is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

The analytic decision‐making preference model to evaluate the disaster readiness in emergency departments: The A.D.T. model

In recent years, a series of important emergencies have been taken place worldwide in industrial plants. After the occurrence of a disaster, it is essential to activate the correct emergency procedures. Particularly, it is important to direct people injured in hospitals which are able to handle emergencies. Thus, nowadays, the emergency services require a management process starting from the disaster moment to the involvement of all actors participating in the process to provide integral, safe, and quality attention. The aim of this study is to help hospitals become better prepared for major disasters and public health emergencies and to evaluate the readiness of emergency departments for a disaster situation. A hybrid model called the “analytic decision‐making preference model” based on analytic hierarchy process, decision‐making trial and evaluation laboratory, and technique for order of preference by similarity to ideal solution methods is proposed. Analytic hierarchy process is used to determine the criteria and subcriteria weights. Then, decision‐making trial and evaluation laboratory is used to evaluate interdependence between criteria and subcriteria. After this, technique for order of preference by similarity to ideal solution is applied to rank the emergency departments from highest to lowest according to their closeness coefficient. A real‐life application in Colombia is presented.     

An Adaptive Algorithm for Pairwise Comparison‐based Preference Measurement

The Pairwise Comparison‐based Preference Measurement (PCPM) approach has been proposed for products featuring a large number of attributes. In the PCPM framework, a static two‐cyclic design is used to reduce the number of pairwise comparisons. However, adaptive questioning routines that maximize the information gained from pairwise comparisons promise to further increase the efficiency of this approach. This paper introduces a new adaptive algorithm for PCPM, which accounts for several response errors. The suggested approach is compared with an adaptive algorithm that was proposed for the Analytic Hierarchy Process as well as a random selection of pairwise comparisons. By means of Monte Carlo simulations, we quantify the extent to which the adaptive selection of pairwise comparisons increases the efficiency of the respective approach. Copyright © 2011 John Wiley & Sons, Ltd.     

An investigation of the role of scale values in the DS/AHP method of multi‐criteria decision making

DS/AHP is a method of multi‐criteria decision making based on the Dempster–Shafer theory of evidence and the analytic hierarchy process. Central to the utilization of DS/AHP is the composing of preference judgements on identified groups of decision alternatives (DA) across a number of criteria against all the DA present in the problem in question. This paper exposits a series of results whose objectives are to aid in the development of an effective set of preference scale values for use within DS/AHP. These results relate directly to the concomitant level of ignorance (uncertainty) with the judgements made on a single criterion. Two particular directions of investigation are undertaken, firstly in determining the necessary number of scale values available and secondly finding the necessary differences between scale values, dependent on whether an arithmetic or geometric progression is the basis for the scale values. Through an example, the implications and utilization of these results within DS/AHP are illustrated. Copyright © 2003 John Wiley & Sons, Ltd.     

Scale horizons in analytic hierarchies

In the light of the many criticisms to which the analytic hierarchy process (AHP) of Saaty has been subjected, the authors have produced a refined version, the modified analytic hierarchy process. This paper develops further the ideas behind the modified process and illustrates with examples some of the difficulties in the AHP and their resolution.     

Aggregating preference rankings: An AHP-based approach

The problem considered here involves the selection of an alternative by a group of decision makers in a context that involves the aggregating of votes from a preferential ballot. A popular approach for solving such problems is the well-known weighting problem formulation. However, with such a formulation two issues become of critical importance: (a) the weights should reflect the decision-making group's belief on the importance of each rank position and (b) the weights should accord each alternative a fair (if not its best) assessment. Many researchers have studied this problem and proposed various solution strategies. None of these strategies, however, appears to have adequately addressed both issues. The objective of this research is to develop a group decision-making model that solves the problem in a manner that adequately addresses the two critical issues identified, as well as allows for sensitivity analysis and is fairly robust with respect to the various paradoxes identified in voting systems.