Scale sensitivity in the multiplicative AHP and SMART

We consider first a variant of the analytic hierarchy process (AHP) with a one-parametric class of geometric scales to quantify human comparative judgement and with a multiplicative structure: logarithmic regression to calculate the impact scores of the alternatives at the first evaluation level and a geometric-mean aggregation rule to calculate the final scores at the second level. We demonstrate that the rank order of the impact scores and final scores is scale-independent. Finally we show that the multiplicative AHP is an exponential version of the simple multi-attribute rating technique (SMART). In fact, the multiplicative AHP is concerned with ratios of intervals on the dimension of desirability, whereas SMART analyses differences in the corresponding orders of magnitude.     

The assignment of scores for output‐based research funding

This paper considers the assignment of scores to research output items, such as articles, books, contributions to conference proceedings, doctoral dissertations, etc., under four distribution criteria: the advancement of pure and applied scientific research, the advancement of innovative problem solving, the dissemination of scientific knowledge, and the coverage of the cost of the research. These scores are to be used in the allocation of research funds to the faculties of a university. The present paper describes the experiments carried out within the framework of the Decision Analysis and Support Project of the International Institute of Applied Systems Analysis, Laxenburg, Austria. It summarizes the vivid discussions triggered by the experiment, and it also presents the results of an additional experiment. Copyright © 1999 John Wiley & Sons, Ltd.     

The Multiplicative AHP,SMART and ELECTRE in a Common Context

This paper presents a comparative study of three popular methods for multicriteria decision analysis based on a particular model of human preferential judgement. Since decisions are invariably made within a given context, we model relative preferences as ratios of increments or decrements in an interval on an axis of desirability. Next we sort the ratio magnitudes into a small number of categories, represented by numerical values on a geometric scale. We explain why the analytic hierarchy process (AHP) and the French collection of ELECTRE methods, typically based on pairwise comparison methods, are concerned with categories of ratio magnitudes, whereas the simple multiattribute rating technique (SMART) essentially uses orders of magnitude of these ratios. This phenomenon provides a common basis for the analysis of the methods in question and for a cross-validation of their results. We illustrate the approach via a well-known case study, the choice of a location for a nuclear power plant. We conclude by discussing the scope of the comparative study. © 1997 John Wiley & Sons, Ltd.     

On the evaluation and application of different scales for quantifying pairwise comparisons in fuzzy sets

One of the most critical issues in many applications of fuzzy sets is the successful evaluation of membership values. A method based on pairwise comparisons provides an interesting way of evaluating membership values. That method was proposed by Saaty, almost 20 years ago, and since then has captured the interest of many researchers around the world. However, recent investigations reveal that the original scale may cause severe inconsistencies in many decision-making problems. Furthermore, exponential scales seem to be more natural for humans to use in many decision-making problems. In this paper two evaluative criteria are used to examine a total of 78 scales which can be derived from two widely used scales. The findings in this paper reveal that there is no single scale that can outperform all the other scales. Furthermore, the same findings indicate that a few scales are very efficient under certain conditions. Therefore, for a successful application of a pairwise-comparison-based method the appropriate scale needs to be selected and applied.     

Problem formulation for multi-criteria decision analysis: report of a workshop

This paper reports on a workshop on Problem Formulation in Multi-Criteria Decision Analysis held at SPUDM97. The focus of the workshop was the problem formulation phase which occurs between the analyst meeting a person with a ‘mess’ and the time he or she begins to analyse a structured problem with several alternatives scored against several attributes or criteria. The objectives were: to share experience on procedures which might be transferable between the methodologies; to demonstrate different skills used by the analyst in structuring decision problems; and to catalyse a discussion on the problem formulation phase of an analysis. Three analysts, who generally approach problems using multiattribute methods, addressed the same problem. The problem used was constructed to be realistic to three decision makers, who had been trained in the issues of concern. There were two sessions. Each analyst was assigned a decision maker and formulated the problem independently in the first session, held in parallel. They were each observed by two observers and many of the audience at the workshop. The three formulations were presented along with the comments of the observers and discussed at a second plenary session. This paper reports the three formulations and observations, remarking on the ‘tricks of the trade’ employed by the analysts in formulating the problem. The analysts also describe their thinking and their aims in adopting their approach and style of interaction. More general remarks on the process of decision analysis are also offered. © 1998 John Wiley & Sons, Ltd.     

Letter to the editor,Schools on Islands,a journal as a Ferry

In an electronic brainstorming session, experts and users of methods for multi-criteria decision analysis discussed editorial policies for a journal which is confronted with the conflicts between isolated schools of thought. The present paper describes the session and highlights how experts in multi-criteria decision analysis view the applications of their own methods on their own decision problems.