Eng Ung Choo

An interactive weighted Tchebycheff procedure for multiple objective programming

The procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted Tchebycheff metric. Using ‘filtering’ techniques, maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration. The procedure has the advantage that it can converge to non-extreme final solutions. Especially suitable for multiple objective linear programming, the procedure is also applicable to integer and nonlinear multiple objective programs.

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.

Pseudolinearity and efficiency

First order and second order characterizations of pseudolinear functions are derived. For a nonlinear programming problem involving pseudolinear functions only, it is proved that every efficient solution is properly efficient under some mild conditions.

Bicriteria linear fractional programming

As a step toward the investigation of the multicriteria linear fractional program, this paper provides a thorough analysis of the bicriteria case. It is shown that the set of efficient points is a finite union of linearly constrained sets and the efficient frontier is the image of a finite number of connected line segments of efficient points. A simple algorithm using only one-dimensional parametric linear programming techniques is developed to evaluate the efficient frontier.

An interactive algorithm for multicriteria programming

Abstract An interactive algorithm for general multicriteria programming is proposed. The decision maker merely selects his most preferred point amongst presented alternatives. The algorithm ensures that the alternatives generated in each iteration are evenly distributed over the desired neighbourhood of the efficient frontier. The algorithm was motivated by the need for solutions to the multiple linear fractional problem and is shown to have a particularly simple and easy to implement structure in this case. A discussion is included of why this problem is important and of how it arises in practice, particularly in financial problems.

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.

Proper Efficiency in Nonconvex Multicriteria Programming

Proper efficient solutions of nonconvex vector maximum problems can be generated by solving a parametric family of ordinary nonlinear programs. This parametric scheme follows from the characterization of proper efficiency by an extended form of the generalized Tchebycheff norm.

Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem

Abstract This paper proposes a new linear programming approach to solve the two-group classification problem in discriminant analysis. This new approach is based on an idea from cluster analysis that objects within the same group should be more similar than objects between groups. Consequently, it is desirable for the classification score of an object to be nearer to its mean classification score, but further from the mean classification score of the other group. This objective is accomplished by minimizing the total deviation of the classification scores of the objects from their group mean scores in a linear programming approach. When applied to an actual managerial problem and simulated data, the proposed linear programming approach performs well both in groups separation and group-membership predictions of new objects. Moreover, this new approach has an advantage of obtaining more stable classification function across different samples than most of the existing linear programming approaches.