Research And Application Of Grey Clustering Model With Whitenization Function Based On Interval Grey Number

As the economy, society and science technology developing, the complexity of problems isincreasing. Grey clustering model with whitenization function based on interval grey number isstudied to solve uncertainty problem. Firstly, the whitenization function whose turn point is intervalgrey number is constructed. And solving methods and results for whitenization function with intervalgrey number are given. Secondly, a sorting algorithm for continuous interval grey number based onpossibility degree is put forward. Scheduling problem for interval grey clustering coefficient is solved.Thirdly, using the grey clustering model with interval whitenization function evaluate thedevelopment of core competencies for private enterprise in Xuchang City. Main tasks are asfollowing:(1) Aiming at the situation that the turn point of the whitenization function must be real number,the method of building and calculating the function when the turn point is an interval grey number isbring forward. The function with interval gray number is constructed through defining thestandardized methods of the interval grey number. And the expression of the whitenization functionwith interval grey number is given. Then discussing the two circumstances that there is only oneinterval grey number in the piecewise curve of the whitening function or two endpoints are bothinterval grey numbers. At last, the expression of whitenization function is given when four turn pointsare all interval grey numbers.(2) In connection with the sorting algorithm for interval grey number of continuous type, asorting algorithm for continuous interval grey number based on possibility degree is proposed. Thepoint possibility degree function which used to offer the comparison between the interval grey numberand real number was constructed, which is used to calculate the possibility degree function whichrepresented the comparison between two interval grey numbers. Then the function expression of sixdifferent positional relationship between the two interval grey number is solved. The possibilitydegree function contains the characteristics such as complementary, transitivity and equivalence.(3) According to research findings and literature, the indicator system to evaluate the corecompetencies for the fourteen companies in Xuchang city. The grey clustering model with intervalwhitenization function is used to appraise it. Validity and feasibility of the model is test.