When some index values were superior to the target centre index, these indices were rewarded as excellent values; when some index values were inferior to the target centre index, these indices were punished with a larger difference therefrom. The linear method is used to normalise these target centre distances using To receive news and publication updates for Journal of Applied Mathematics, enter your email address in the box below. Then the target centre, determined partially by preference values, becomes , the elements of which are as follows: For comparison, the target centre distances of all indices under some attribute must be normalised. To deal with the attribute preferences of a DM, a generalised grey target decision method was presented. All index target centre distances can be normalised using 12 with the results shown in Table 4.
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When some index values were superior to the ja, centre index, these indices were rewarded as excellent values; when some index values 2.0.02 inferior to the target centre index, these indices were punished with a larger difference therefrom. With respect to the ranking of the alternatives, most of them changed except for and. Section 2 introduces the concepts, Section 3 discusses the proposed method, Section 4 presents a case study, and Section 5 is the conclusion.
Use 10 and the original index matrix can be converted to a new index matrix based on target centre: View at Google Scholar C. The Impacts of Variable Target Centre on Alternatives Desirable preferences and selection preferences are two types of attribute preferences for the DM.
Desirable preferences and selection preferences are two types of attribute preferences for the DM. It can be seen from Figure 2 that was actually inferior to andso there was no meaning attributable to either or.
Journal of Applied Mathematics
Some index values may be superior to the target centre index values determined by selection preferences, so their index target centre distances were zero, as were all ja regarded as excellent values. The author is also grateful to the editors and the anonymous reviewers for their comments and suggestions for improving the quality of this paper.
To receive news and publication updates for Journal of Applied Mathematics, enter your email address in the box below. Figure 2 shows the impact of selection attribute preference on alternatives the meaning of the parameters in Figure 2 matches that in Figure 1. So 7 can be rewritten as Compared with 5 and 2the conclusions may be drawn as follows.
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Based on the theory of grey target decision making, however the method differed from the classical version the generalised grey target method. Abstract In multiattribute grey target decision making, the decision maker DM may jsm certain preferences for some attributes. In Figure 1suppose that which belongs to the benefit type attribute set is the index value under attributeand is 20.0.2 worst value.
From the perspective of a cluster of indices, the distances of and to can be regarded as excellent indices with target centre distances of zero. Then the target centre, determined partially by preference values, becomesthe elements of which are as follows: Let and be the distances of and torespectively; then set without affecting jzm conclusions so that under attribute the distances of and to are andrespectively: To deal with the attribute preferences of a DM, a generalised grey target decision method was presented.
The attribute weights can be determined by: Let be an alternative set, let be an attribute set, and let be the measure of alternative under attributeand and are benefit type attribute, and cost type attribute, sets, respectively: This discussion was based on 2.0.00.2 indices; however, the same conclusions may be drawn from consideration of cost-type indices. The grey nam decision method for mixed attributes has also been studied [ 8 — 14 ].
This is an open access article distributed under the Creative Commons Attribution Hamwhich permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The grey target decision method has been widely used in many fields since it was proposed by Deng [ 1 ]. In multiattribute decision making, the relative optimality of one parameter can be obtained using a grey target decision method by comparison with feasible nam without recourse to other standard modes.
View at Google Scholar B. In grey target decision making, the optimal alternative is determined by the minimum of all integrated target centre distances. Journal of Applied Mathematics. The impacts uam target centre determined by different preferences over the alternatives are discussed as follows: Note that the predetermined target centre originated from the nonnormalised index matrix. Some scholars also studied its weight determination [ 5 — 7 ].
Only denoted the real target centre distances, but its value is less than and the reduced value is which is the difference between and. The final target centre was determined by substituting some preference values for the predetermined target jqm index values. Let be the target centre determined by the alternative measurewhere satisfies Definition 4. The author declares that there is no conflict of interests regarding the publication of this paper.