• Asia pacific journal of information systems
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• v.16 no.1
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• pp.85-101
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• 2006

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.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.273-278
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• 2009

The determination of the associated weights in the theory of ordered weighted averaging (OWA) operators is one of the important issue. Recently, Wang and Parkan [Information Sciences 175 (2005) 20-29] proposed a minimax disparity approach for obtaining OWA operator weights and the approach is based on the solution of a linear program (LP) model for a given degree of orness. Recently, Liu [International Journal of Approximate Reasoning, accepted] showed that the minimum variance OWA problem of Fuller and Majlender [Fuzzy Sets and Systems 136 (2003) 203-215] and the minimax disparity OWA problem of Wang and Parkan always produce the same weight vector using the dual theory of linear programming. In this paper, we give an improved proof of the minimax disparity problem of Wang and Parkan while Liu's method is rather complicated. Our method gives the exact optimum solution of OWA operator weights for all levels of orness, $0\leq\alpha\leq1$, whose values are piecewise linear and continuous functions of $\alpha$.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.537-541
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• 2006

In this note, we give an elementary simple proof of the main result of $Full{\acute{e}}rand$ Majlender [Fuzzy Sets and systems 124(2001) 53-57] concerning obtaining maximal entropy OWA operator weights.

• Journal of Navigation and Port Research
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• v.31 no.6
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• pp.537-543
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• 2007

It's an important part to calculate the weights between criterions and to aggregate the decision inputs in a MCDM(Multi criterion decision making) This paper presents a method for aggregation cf decision inputs and application to the MCDM. We incorporate the fuzzy set theory and the basic nature of subjectivity due to ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environments. To obtain the scoring that corresponds to the best alternative or the ranking of the alternatives, we need to use a total order for the fuzzy numbers involved in the problem. In this article, we consider a definition of such a total order, which is based on two subjective aspects: the degree of optimism/pessimism reflected with the ordered weighted averaging(OWA) oprators. A numerical example, expecially location analysis for anchorage area, is given to illustrate the approach.