An empirical comparison of three variants of the AHP and two variants of conjoint analysis

This paper provides an empirical comparison of two methods of attribute valuation: the analytic hierarchy process (AHP) and conjoint analysis. Variants within each approach are also examined. The results of two empirical studies indicate that the methods differ in their predictive and convergent validity. Within the AHP methods no significant difference in predictive validity was found. Within the conjoint methods, the ranking method significantly outperformed the rating method. The difference in predictive validity between the AHP and conjoint methods was significant in the second study but not in the first study, suggesting superior performance of the AHP over conjoint analysis in complex problems. Copyright© 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.     

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.     

Performance oriented task-resource mapping and scheduling in fog computing environment

Resource allocation and task scheduling is a complex task in fog computing environment because of the inherent heterogeneity among the fog devices. The proposed work attempts to solve the problem by using the popular multi criteria decision making methods such as AHP and TOPSIS. The goal of this paper is to propose a model for performance oriented task - resource mapping in a fog computing environment. MIPS, RAM & storage, uplink latency, downlink latency, uplink bandwidth, downlink bandwidth, trust, cost per MIPS, cost per memory, cost per storage and cost per bandwidth are the various performance characteristics considered in this work for task – resource mapping. Two different multi-criteria decision making methods are employed in order to assess the performance characteristics of the fog devices. In the first method, Analytic Hierarchy Process (AHP) is used for both priority weight calculation and ranking of fog devices. In the second method, AHP is used for priority weight calculation, based on the weights yielded by AHP, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) algorithm is executed in order to rank the fog devices. Then the fog devices can be allocated to the tasks based on its rank. Furthermore, a motivational example is also demonstrated to validate the proposed method. Simulation results show that the proposed technique exhibits superior performance over other scheduling algorithms in the fog environment by incorporating performance, security, and cost metrics into scheduling decisions.     

A re-examination of the algebraic properties of the AHP as a ratio-scaling technique

The Analytic Hierarchy Process (AHP) ratio-scaling approach is re-examined in view of the recent developments in mathematical psychology based on the so-called separable representations. The study highlights the distortions in the estimates based on the maximum eigenvalue method used in the AHP distinguishing the contributions due to random noises from the effects due to the nonlinearity of the subjective weighting function of separable representations. The analysis is based on the second order expansion of the Perron eigenvector and Perron eigenvalue in reciprocally symmetric matrices with perturbations. The asymptotic distributions of the Perron eigenvector and Perron eigenvalue are derived and related to the eigenvalue-based index of cardinal consistency used in the AHP. The results show the limits of using the latter index as a rule to assess the quality of the estimates of a ratio scale. The AHP method to estimate the ratio scales is compared with the classical ratio magnitude approach used in psychophysics.     

A note on the use of goal programming for the multiplicative AHP

The main aim of this paper is to identify the opportunities of utilizing goal programming (GP) in the multiplicative analytic hierarchy process (MAHP). It starts with the issue of weight derivation from judgemental matrices. The use of GP for the weight derivation problem is not new, but GP is viewed in this paper from the perspective of augmenting the capabilities of the widely used row geometric mean method (RGMM) of the logarithmic least squares technique (LLST). Different possible approaches using GP are discussed. It is shown that the formulation of the GP problem can be easily modified to provide the same weights as those of the LLST. While this proposed GP technique is not superior to the RGMM in terms of computational ease or speed, it is quite useful in solving certain other problems of the MAHP, such as interval judgements and missing judgements, which cannot be readily solved by the RGMM. The proposed technique provides extensive scope for utilizing the vast literature on non-linear programming, say, for conducting sensitivity analysis. It also has the potential to be useful to more complicated issues of the MAHP, such as group decision making and interlevel dependence, hitherto little explored areas of the MAHP. © 1997 John Wiley & Sons, Ltd.     

A generalization of the representational change theory from insight to non-insight problems: the case of arithmetic word problems

This paper provides evidence for a possible generalization of Knoblich and colleagues’ representational change theory [Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, 1534-1555; Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem. Memory and Cognition, 29, 1000-1009] outside its original scope of application. While this theory has been proposed to explain insight problem solving, we demonstrate here that its main concepts, namely, constraint relaxation and chunk decomposition, are applicable to incremental problem solving. In a first experiment, we confirm, as already shown by problem solving and reasoning researchers, that individuals avoid the construction of alternative representations of the problems when possible. In the second and third experiments, we show that alternative representations of arithmetic problems are easier to construct and maintain when they violate constraints of narrow rather than wide scope. The specificity of insight problem solving is discussed in the light of these new findings.     

Power Relations and Group Aggregation in the Multiplicative AHP and SMART

The relative power of the members in a group of decision makers can be incorporated in the multiplicative AHP via power coefficients in the logarithmic least squares whereby we analyse the pairwise comparison matrices. When each decision maker judges every pair of alternatives under each of the criteria, aggregation over the criteria and over the decision makers proceeds via a sequence of geometric-mean calculations which can be carried out in any order, at least with predetermined criterion weights and power coefficients. Hence, since we preserve the rank order of the alternatives, we avoid a deficiency of the original AHP. We also consider SMART, an additive method which is logarithmically related to the multiplicative AHP so that power relations can easily be incorporated in it. Finally, in order to illustrate the proposed model, we analyse a generalized version of the well-known example of Belton and Gear as well as the power relations between member countries of the European Community. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 155–165 (1997) No. of Figures: 0. No. of Tables: 6. No. of References: 23.     

Clustering,dependence and ratio scales in AHP: Rank reversals and incorrect priorities with a single criterion

In the analytic hierarchy process, it is often thought that rank reversals cannot occur in a single-criterion problem. This paper demonstrates that if it is necessary to cluster items under a single criterion, such reversals are possible. The reversals occur prior to aggregating across clusters and are caused by a failure to make reference to the alternatives when performing criteria comparisons. Rank reversals, however, are only a symptom of the problem. The real problem is a failure to calibrate global weights to a common scale which spans different clusters. Even in the absence of reversals, aggregated weights from the AHP's relative mode of measurement can fail to maintain composite ratio relationships.     

On the Proper Interpretation and Impact of the AHP Axiom of Independence in Single-Criterion and Multiple-Criteria Problems

Some authors have proposed that the analytic hierarchy process (AHP) axiom of independence be relaxed to accommodate observations drawn from (a) examples of pairwise comparisons of alternatives in clusters in single-criterion AHP problems and (b) examples of problems in which the criteria have the same underlying measurement and both the achievement of the goal and the alternatives are measured objectively. We show that the illustrations given are actually single-criterion problems according to the AHP. Thus the AHP axiom of independence is inapplicable in both situations and therefore not violated. We also consider the consequence of failure to distinguish between a criterion as an attribute of alternatives and cluster of alternatives, the two being different in the hierarchic structure. Finally, we discuss transformable problems, which look like multicriteria problems but are actually single-criterion problems, and how failure to recognize this fact may lead to incorrect syntheses and false conclusions.     

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.     

Teenage pregnancy: a theoretical analysis of a social problem

This paper begins by contrasting the two basic ways of defining a social problem (i.e., as a "problem" in society or of society). The implications of these two definitions are discussed within the context of the various approaches which have emerged from each. A typology is then developed which allows these divergent approaches to be synthesized into three broad categories (Social Disorganizational, Social Definitional, and Social Organizational). This typology helps to further clarify the implications of isolating certain noxious conditions (whether personal or social) and conceptualizing them as social problems. These implications for the emergence, scope, and possible solution to the problem of teenage pregnancy are discussed. The paper concludes with a theoretical critique that leaves little room for optimism about the piecemeal solutions to teenage pregnancy offered by either the social disorganizational or the social definitional approaches, yet it recognizes the unlikely prospects that the holistic solution is likely to be adopted soon. The paper thus concludes that this problem is likely to be with us for some time to come, and the best that we can hope to do is to treat the symptoms.     

Using the Analytic Hierarchy Process to Analyze Multiattribute Decisions

Since its introduction a decade ago, the Analytic Hierarchy Process (AHP) has been used by decision makers in many contexts. The vast majority of these applications has involved allocating resources or making choices from among alternatives. This article discusses how AHP may be used in a different manner: to assist researchers in the analysis of decisions. AHP is briefly compared with other decision-analysis techniques, such as multiattribute utility measurement, conjoint measurement, and general linear models (regression and analysis of variance). Some of the possible insights into decision processes that can be obtained using AHP are illustrated with data gathered from practicing auditors of financial statements.     

II—On Modelling Vagueness—and on not Modelling Incommensurability

This paper defines and analyses the concept of a 'ranking problem'. In a ranking problem, a set of objects, each of which possesses some common property P to some degree, are ranked by P-ness. I argue that every eligible answer to a ranking problem can be expressed as a complete and transitive 'is at least as P as' relation. Vagueness is expressed as a multiplicity of eligible rankings. Incommensurability, properly understood, is the absence of a common property P. Trying to analyse incommensurability in the same framework as ranking problems causes unnecessary confusion.     

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.     

Time complexity and consistency issues in using the AHP for making group decisions

Two different ways of using the AHP in making group decisions are compared and evaluated. The first method combines different experts’ opinions before applying an eigenvalue method to obtain final weights for decision alternatives. The second, in contrast, derives each expert's rating for the decision alternatives before combining them. Both methods take into account the relative importance of different experts in making decisions. Comparison and evaluation of these two methods are made by using two criteria: time complexity and consistency indices. A numerical example is provided to illustrate the use of these two methods, and results of a mathematical simulation are presented for comparing the time complexity in different-sized problems. © 1998 John Wiley & Sons, Ltd.     

A Decision Support System for Prioritizing Investments in an Energy Efficiency Program in Favelas in the City of Rio de Janeiro

This study proposes an integrated qualitative and quantitative assessment of expert opinions aiming at ranking a set of five shantytowns (favelas) located in the city of Rio de Janeiro. These communities are candidates for investments in an energy efficiency program implemented by the local electric utility company. The city, state, and federal governments want to eliminate domination of these areas by organized criminal gangs and present the city as a peaceful metropolis while hosting two big sports events: the soccer World Cup in 2014 and the Olympic Games in 2016. In recent years, some favelas were chosen to be prototypes for an ambitious project to reshape Rio de Janeiro. This involves first sending in special tactics police to drive drug gangs out, then installing the Pacifying Police Unit in the favela. Once security has been established, it is possible to improve general living conditions in these areas, including by providing public services such as health clinics, formal electricity connections and cable television. The core of the energy efficiency program was to convert informal customers to formal ones, because such communities were responsible for approximately 40% of the commercial losses (stolen energy) in the city. The model specification presented in this paper was set up with ten relevant criteria for decision making, identified through an in‐depth interview with the decision maker. The relative importance of the criteria and the performance of each favela regarding each criterion were measured by the Simos method. The preferences resulting from this method were translated into a nine‐point scale. The imprecision of subjective judgment was partially compensated by using a fuzzy analytical hierarchy process. Some criteria were ordinal, such as ‘Fair Relationship with the Community’ and ‘Complexity to Rebuild the Distribution Lines’, whereas other were cardinal, like ‘Percentage of Clients in Default’ and ‘Commercial Loss Due to Energy Theft’. At the end, the model was efficient in ranking the five favelas, therefore contributing to a rational and transparent approach for capital investment in social projects. Copyright © 2014 John Wiley & Sons, Ltd.     

On the psychophysical discriminability of somatosensory nerve action potential patterns with irregular intervals

In this paper we consider the problem of whether or not a series of irregularities in the interpulse intervals in a train of nerve action potentials can be discriminated better than a single gap in a regular train. We also consider the corollary problem-does an increase in the number of impulses in a burst with irregular intervals lead to a decrease in the threshold for irregularity, thus indicating some integrative capacity of the relevant neural decoding mechanism. Answers to these questions are obtained by means of a psychophysical test and are affirmative in both cases. This suggests that the irregularities which have been observed in the intervals between nerve action potentials in animal preparations are true information-carrying codes within a restricted temporal region. Because of certain critical points in the functions relating this sensitivity to the basic frequency of the nerve impulses, a group of seiveral temporal regions is postulated in which time is dealt with differently by the somatosensory system.     

Act first, think later: The presence and absence of inferential planning in problem solving

Planning is fundamental to successful problem solving, yet individuals sometimes fail to plan even one step ahead when it lies within their competence to do so. In this article, we report two experiments in which we explored variants of a ball-weighing puzzle, a problem that has only two steps, yet nonetheless yields performance consistent with a failure to plan. The results fit a computational model in which a solver’s attempts are determined by two heuristics: maximization of the apparent progress made toward the problem goal and minimization of the problem space in which attempts are sought. The effectiveness of these heuristics was determined by lookahead, defined operationally as the number of steps evaluated in a planned move. Where move outcomes cannot be visualized but must be inferred, planning is constrained to the point where some individuals apply zero lookahead, which with n-ball problems yields seemingly irrational unequal weighs. Applying general-purpose heuristics with or without lookahead accounts for a range of rational and irrational phenomena found with insight and noninsight problems.     

The analysis of multitrait-multimethod matrices via constrained components analysis

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to three anonymous reviewers and an associate editor for constructive suggestions on the first version of this paper.