William C. Wedley

A common framework for deriving preference values from pairwise comparison matrices

Pairwise comparison is commonly used to estimate preference values of finite alternatives with respect to a given criterion. We discuss 18 estimating methods for deriving preference values from pairwise judgment matrices under a common framework of effectiveness: distance minimization and correctness in error free cases. We point out the importance of commensurate scales when aggregating all the columns of a judgment matrix and the desirability of weighting the columns according to the preference values. The common framework is useful in differentiating the strength and weakness of the estimated methods. Some comparison results of these 18 methods on two sets of judgment matrices with small and large errors are presented. We also give insight regarding the underlying mathematical structure of some of the methods.

Interpretation of criteria weights in multicriteria decision making

Multicriteria decision making models are characterized by the need to evaluate a finite set of alternatives with respect to multiple criteria. The criteria weights in different aggregation rules have different interpretations and implications which have been misunderstood and neglected by many decision makers and researchers. By analyzing the aggregation rules, identifying partial values, specifying explicit measurement units and explicating direct statements of pairwise comparisons of preferences, we identify several plausible interpretations of criteria weights and their appropriate roles in different multicriteria decision making models. The underlying issues of scale validity, commensurability, criteria importance and rank consistency are examined.

A UNIFIED APPROACH TO AHP WITH LINKING PINS

Abstract Recent work demonstrates the need for paired comparison estimates of criteria in the Analytic Hierarchy Process (AHP) to follow prescribed rules, and for the subsequent analysis to be contingent on these rules. Many different approaches are valid, each reflecting a different rule for criteria comparison. A generalized formula from which valid approaches may be generated is presented, and the connection between these methods and Saatys supermatrix approach is explored.

Combining qualitative and quantitative factors--an analytic hierarchy approach

Abstract The Analytic Hierarchy Process (AHP) provides a general theory of measurement for expressing both tangible and intangible factors. In this paper, intangible or qualitative factors are looked upon as dimensions which we have not yet learned how to measure very well. Through a redundant paired-comparison process. AHP allows us to translate qualitative preferences into ratio scaled data. In addition, the structuring stage of AHP facilitates problem understanding.

Magnitude adjustment for AHP benefit/cost ratios

Abstract A feature of the Analytic Hierarchy Process (AHP) that has not been subject to close scrutiny is its use for benefit/cost analysis. If benefit priorities are divided by project costs to yield benefit points per dollar, then the resulting numbers can be used to allocate program budgets. But if benefit priorities and cost priorities are derived from two separate hierarchies, then it is likely that the ratio of benefit priorities to cost priorities produces misleading results. To correct the situation, adjustments must be made to put the numerator and denominator priorities into commensurate terms.

Maintenance management – an AHP application for centralization/decentralization

The decision to centralize or decentralize different functions of a maintenance department in a plant has not been traditionally made on a systematic and quantitative basis. This paper proposes a systematic model for evaluating different maintenance organizational structures with respect to the objectives of a maintenance department. Based on a group decision process, the model provides step‐by‐step guidelines for the maintenance management and decision makers to go through the evaluation process. A case example is shown, which involves four alternative organizational structures. Examples are given to show the calculation process for grouping the assessments of individual team members and for final analysis towards the evaluation of the organizational alternatives.

Consistency prediction for incomplete AHP matrices

The efficiency of the Analytic Hierarchy Process can be improved if users can establish priorities without completing the entire set of pairwise comparisons. This study develops a methodology for predicting the consistency index and consistency ratio when pairwise comparisons are incomplete. Separate prediction equations are presented for each size of matrix from 5 to 10. These equations can be incorporated into AHP software so that users will have a predicted consistency ratio when making the decision to stop or proceed with more paired comparisons.

Starting rules for incomplete comparisons in the analytic hierarchy process

Entering pairwise comparisons to the Analytic Hierarchy Process (AHP) can be very tedious if the hierarchy is large. Accordingly, techniques exist to derive priorities from incomplete comparisons. This study investigates the effect of different reference items for the first (n - 1) pairwise comparisons of the Incomplete Analytic Hierarchy Process. It analyzes the accuracy of AHP users in estimating the proportions of five colors in a rectangular picture. The empirical results show that significantly greater initial accuracy is achieved if the items are ranked and the lowest ranked item is used as a common referent for the first (n - 1) comparisons.

Linear goal programming in estimation of classification probability

Classification of objects into groups is a common practice in everyday life. Normally, the scores of some pertinent criteria about the objects are available and form the most important factor in the classification decision. Discriminant analysis [4], logistic regression [1,3], and linear goal programming [2,5] are alternative techniques used to determine the criterion weights. Classification with these techniques is based upon the weighted sum of the criterion scores of each object. The classification itself ignores more discriminating information about objects within groups. For example, dividing companies into bankrupt and non-bankrupt groups ignores the fact that the non-bankrupt group contains companies of varying qualities. Thus, it is more appropriate to determine the group membership probabilities for each object instead of just the pure classification into one of the groups. These probabilities can readily be used to discriminate objects within the same group.

The Needs of Small Business Owners: Perceptions of Entrepreneurs and Service Providers

Abstract Many government and private organizations have a stake in increasing the rate of success of new business ventures in Canada. Federal, provincial and municipal governments, private and public banks, educational institutions, chambers of commerce and other organizations provide services with the objective of encouraging entrepreneurship and sustaining new ventures. Are the services offered the ones that owners of startup business require? Do entrepreneurs attribute the same level of importance to start-up assistance as do the providing organizations? The data from this study indicate agreement on the types of venture services needed, but disagreement on how important those services are to startup business managers. Entrepreneurs in different industries rate access to various types of assistance quite differently.