Uncertain Type of Multiple-Attribute Electronic Commerce Investment Decision Model Based on the Close Degree of the Scheme and Its Applications

To deal with the problem of uncertain type of multiple-attribute electronic commerce investment decision whose attribute weights can’t be fully known, a index which measures the decisionmaking plan-close degree was Introduced, and a decision-making model based on the scheme close degree was established. The article analyses the application of the model used in investment decisions.


Introduction
In essence, after determining the comprehensive attribute values of each scheme, multiple-attribute decision making ranks and optimizes the schemes according to their comprehensive attribute values.At presents, the decision making theory and method about the multi-attribute decisions whose attribute weights information is completely known is complete.But in order to deal with the problem of electronic commerce investment decision, decisions made by managers according to their experiences are too subjective, because the weights of factors in the decision making process are difficult to be determined accurately due to the complexity of the economic system and the fluidity of the market situation [1].The article solves the uncertain type of multiple attribute decision making problems part of whose attribute weights information is completely unknown.In the first place, a key indicator-scheme close degree was introduced, and then, a decision making model based on the scheme close degree was given which was one of methods to solve the problem.

Basic Theory
Hypotheses: is the scheme aggregate of the decision making problem; , , , m ω ω ω ω =  is the weight vector of the attribute; 1 0, 1 . H is the attribute weight vector according to the known weight information, Especially, if H is null set, attribute weight is completely unknown.Scheme j x X ∈ , attribute i is measured, and attribute value ij a of j x is got, so decision matrix ( ) i ω is the weight of attribute i u .When weight i ω is certain, the strengths and weaknesses of each scheme can be known by their comprehen- sive attribute value.When i ω is unknown, comprehensively attribute value cannot be got by equation ( 1) [3].
The situation when attribute weight cannot be completely known will be discussed.
In certain , comprehensive attribute values ( ) j z ω are expected to be big.The problem of multi-target decision is thought about.
(MOP) Target function: , this is the optimal solution to the following single-target optimized model: (SOP1) Target function: ( ) is the comprehensive attribute ideal value of scheme j x is the minus comprehensive attribute ideal value of scheme j x is the optimal solution to the following single-target optimized model: (SOP2) Target function: ( ) ( ) , , , , n z z z z z =  are the ideal point and minus ideal point of multi-objective decision problem (MOP) respectively.
The included angle cosine of Scheme comprehensive attribute value vector ( ) The included angle cosine of Scheme comprehensive attribute value vector ( )  and minus ideal point ( ) To consider the comprehensive attribute value of each scheme as one unit, scheme close degree is used.Scheme close degree function is: , , For random , the scheme comprehensive attribute value vector as ( ) s ω gets larger, otherwise, the scheme comprehensive attribute value vector will be more similar to minus ideal points when schemes are far away from their optimal condition [4].So we can consider scheme close degree as a reasonal indicator to measure decision schemes.We maximise this indicator and establish the following single-objective optimised model: (SOP3) Target function: , (H is already known) The optimal attribute weight vector * ω can be gotten, and then the corresponding scheme comprehensive at- tribute value vector ( ) * z ω can also be gotten.Schemes are ranked and sorted by their comprehensive attribute value.
According to the above-mentioned theory, an uncertain type multi-objective decision method based on scheme close degree is given.The following are specific Steps: 1) Decision matrix

Application Exemples
There are four e-commerce investment schemes x 1 , x 2 , x 3 , x 4 to be measured.Attributes are company strategy u 1 , market scale u 2 , risk u 3 , capital u 4 , strengths of rivals u 5 and scope u 6 [5].Attribute values of each schemes are shown in Table 1 2) Use the following formula to regulate matrix A, T 1 , T 2 are sets of benefit-type and cost-type respectively.Standardization matrix is gotten: ( )   x x x x > > > .The optimal scheme is 1 x .

Conclusion
Decision-making model based on the scheme close degree can determine what is the optimal plan in the lack of

3 ) 4 )
Use model (SOP1) and (SOP2) to get ideal point Use equation (2) to calculate a, b; 5) Solve single-objective decision model (SOP3) and get optimal solution * ω , close degree ( ) * z ω and relevant scheme comprehensive attribute value vector ( ) ( and sort schemes by their comprehensive attribute value.

Table 1 .
. Attributes value of each scheme.3 and u 5 are cost-type attributes; u 1 , u 2 , u 4 and u 6 are benefit-type attributes.The weight i u