Asia pacific journal of information systems

The Korea Society of Management Information Systems (한국경영정보학회)
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The Ordered Weighted Averaging (OWA) Operator Weighting Functions with Constant Value of Orness and Application to the Multiple Criteria Decision Making Problems

순위가 있는 가중치 평균 방법에서 일정한 수준의 결합력을 갖는 가중치 함수의 성질 및 다기준의사결정 문제에의 활용

  • Published : 2006.03.31
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Abstract

Actual type of aggregation performed by an ordered weighted averaging (OWA) operator heavily depends upon the weighting vector. A number of approaches have been suggested for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has such properties as rank-based weights and constant value of orness, irrespective of number of objectives aggregated. Specifically, we propose four analytic forms of OWA weighting functions that can be positioned at 0.25, 0.334, 0.667, and 0.75 on the orness scale. The merits for using these weights over other weighting schemes can be mentioned in a couple of ways. Firstiy, we can efficiently utilize the analytic forms of weighting functions without solving complicated mathematical programs once the degree of orness is specified a priori by decision maker. Secondly, combined with well-known OWA operator weights such as max, min, and average, any weighting vectors, having a desired value of orness and being independent of the number of objectives, can be generated. This can be accomplished by convex combinations of predetermined weighting functions having constant values of orness. Finally, in terms of a measure of dispersion, newly generated weighting vectors show just a few discrepancies with weights generated by maximum entropy OWA.

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References

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