Abstract
In the field of decision-making, for the multiple attribute decision-making problem with the partially unknown attribute weights, the evaluation information in the form of the intuitionistic fuzzy numbers, and the preference on alternatives, this paper proposes a comprehensive decision model based on the intuitionistic fuzzy cross entropy distance and the grey correlation analysis. The creative model can make up the deficiency that the traditional intuitionistic fuzzy distance measure is easy to cause the confusion of information and can improve the accuracy of distance measure; meanwhile, the grey correlation analysis method, suitable for the small sample and the poor information decision-making, is applied in the evaluation. This paper constructs a mathematical optimization model of maximizing the synthesis grey correlation coefficient between decision-making evaluation values and decision-makers’ subjective preference values, calculates the attribute weights with the known partial weight information, and then sorts the alternatives by the grey correlation coefficient values. Taking venture capital firm as an example, through the calculation and the variable disturbance, we can see that the methodology used in this paper has good stability and rationality. This research makes the decision-making process more scientific and further improves the theory of intuitionistic fuzzy multiple attribute decision-making.
Highlights
Professor Zadeh [1] pioneered the concept of fuzzy sets and opened up a new area for people to deal with the fuzzy information in 1965
In the field of decision-making, for the multiple attribute decision-making problem with the partially unknown attribute weights, the evaluation information in the form of the intuitionistic fuzzy numbers, and the preference on alternatives, this paper proposes a comprehensive decision model based on the intuitionistic fuzzy cross entropy distance and the grey correlation analysis
Suppose the decision-makers have some preference on alternatives Ai (i = 1, 2, . . . , m) and the preference values are noted by the intuitionistic fuzzy numbers oi = (i = 1, 2, . . . , m); we adopt the optimization model based on the intuitionistic fuzzy cross entropy and the grey correlation analysis method to find the optimum solution among the alternatives with preference
Summary
Professor Zadeh [1] pioneered the concept of fuzzy sets and opened up a new area for people to deal with the fuzzy information in 1965. In view of the above analysis, we propose a comprehensive decision model based on the intuitionistic fuzzy cross entropy distance and the grey correlation analysis to solve the problem of the intuitionistic fuzzy multiple attribute decision-making with preference on alternatives in this paper, which makes up the deficiency of causing the information confusion for the traditional intuitionistic fuzzy distance measure, improves the accuracy of the distance measure, solves the attribute weights by combining with the grey correlation analysis suitable for the small sample and the poor information decision-making, setting up the mathematical programming model with the maximum synthesis grey correlation coefficient between the evaluation value and the subjective preference value of the decision-makers, and sorts the alternatives according to the change of the grey identification coefficients to demonstrate the stability. The validity of the model is proved by the example of a venture capital firm
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