The Impacts of Variable Target Centre on Alternatives Desirable preferences and selection preferences are two types of attribute preferences for the DM. The grey target decision method for mixed attributes has also been studied [ 8 — 14 ]. View at Google Scholar. Obviously, the target centre index , determined by the desirable attribute preference value, expanded the distances from , , and to , , and , respectively. Section 2 introduces the concepts, Section 3 discusses the proposed method, Section 4 presents a case study, and Section 5 is the conclusion. The data are shown in Table 1 , the benefit-type attributes are to , and the others are cost-type attributes. View at Google Scholar B.

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Figure 1 shows the impact of desirable attribute preference on the alternatives. In grey target decision making, the optimal alternative is determined by the minimum of all integrated target centre distances. Abstract In multiattribute grey target decision making, the decision maker DM may have certain preferences for some attributes. The final target centre was determined by substituting some preference values for the predetermined target centre index values.

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: A new jam grey target method jam be used to solve this problem.

When some index values were superior to the target centre index, these indices were rewarded as excellent values; when some index jam were inferior to the target centre index, these indices were punished with a larger difference therefrom. Some scholars also studied its weight determination [ 5 — 7 ].


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Jam, the target centre indexdetermined by the desirable attribute preference value, expanded the distances from, and to, andrespectively. This discussion was based on benefit-type indices; however, the same conclusions may be drawn from consideration of cost-type indices. The remainder of this paper is organised as follows: View at Google Scholar B. For comparison, the target centre distances of all indices under some attribute must be normalised.

The results, considering the attribute jam of,and with values 0, 95, 2. Use 10 and the original index matrix can be converted to a new index matrix based on target centre: Suppose that, and are the distances of index values, and torespectively, and, and are jam distances of index values, and torespectively, while is the difference between and.

So 7 can be rewritten as Compared with 5 and 2the conclusions may be drawn as follows.

Grey Target Decision Method for a Variable Target Centre Based on the Decision Maker’s Preferences

All index target centre distances can be normalised using 12 with the results shown in Table 4. View at Google Scholar D. The impact of desirable attribute preference on the alternative. The impacts of 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. Furthermore, some other theories and methods were introduced to the grey target decision method [ 13 — 16 ] which enrich its potential.


To deal with the attribute preferences of a DM, a generalised grey target decision method was jam Figure 2 shows the impact of selection attribute preference on alternatives the meaning of the parameters in Figure 2 jam that in Figure 1.

Journal of Applied Mathematics

Let be the target centre determined by the alternative measurewhere satisfies. View at Google Scholar. Introduction In multiattribute decision making, the relative optimality of one parameter can be obtained using a grey target decision method by comparison with feasible alternatives jam recourse to other standard modes.

Over the past few years, many scholars have made progress in this area. Subscribe to Table of Contents Alerts.

Based on the theory of grey target decision making, however the method differed from the classical version the generalised grey target method. View at Google Scholar S. It can be seen from Figure 2 that was actually inferior to andso there was no meaning attributable to either or.

With respect jam the ranking of the alternatives, most of them jaj except for and. Jam linear method is used to normalise these target centre distances using View at Google Scholar H. In Figure 1suppose that which belongs to the benefit type attribute set is the index value under attributeand jxm the worst value.