Research On Grey Target Decision-making Model On Three-parameter Interval Grey Number Based On Possibility Functions Of Different Shapes

Decision-making behavior is an inevitable behavior in people’s daily life.With the increase of uncertainty in the decision-making process,the decision information showed the grey uncertainty characteristics of “small data” and “poor information”.On this basis,grey decision-making method became an important method to solve the uncertain decision-making problem because of its unique superiority.Because of the complexity and uncertainty of the objective environment,using three-parameter interval grey number to describe the decision problem was more in line with the real situation.So,in this paper,three-parameter interval grey number was used to describe decision information.Based on the original three-parameter interval grey number decision,a new three-parameter interval grey number distance measurement method was proposed by combining the value possibility of each point of three-parameter interval grey number with the possibility functions of attribute value.The inverted “U”-shaped,“U”-shaped and monotonic three-parameter interval grey number grey target decision-making models were constructed.The specific research contents of this paper were as follows.(1)Establishing a grey target decision-making model with inverted “U”-shaped three-parameter interval grey number.First of all,in view of the case that the attribute value was inverted “U”-shaped three-parameter interval grey number,the definition and the possibility function of inverted “U”-shaped three-parameter interval grey number were explored,which laid a foundation for the following data processing.Secondly,in view of the shortcomings of the existing distance measurement formula of three-parameter interval grey number,the distance measurement formula of inverted “U”-shaped three-parameter interval grey number was given.Then,a grey target decision-making model with inverted“U”-shaped three-parameter interval grey number was constructed.Attribute values with different meanings,dimensions and attributes were treated by uniform effect measure method.According to the principle of grey entropy and maximum entropy,the goal programming model was established and the attribute weights were determined.Finally,selected the quasi-normal distribution curve as the special shape of inverted “U”-shaped three-parameter interval grey number possibility function.And the model was verified by an example of ice disaster risk management in the Yellow River.(2)Establishing a grey target decision-making model with “U”-shaped three-parameter interval grey number.First of all,in view of the case that the attribute value was “U”-shaped three-parameter interval grey number,the definition of “U”-shaped three-parameter interval grey number was given.And the possibility function of “U”-shaped three-parameter interval grey number was explored.Secondly,the distance measurement formula of “U”-shaped three-parameter interval grey number was given.Then,a grey target decision-making model with “U”-shaped three-parameter interval grey number was constructed.Finally,taking the number of concurrent purchases of electronic resources in a university library as an example,the model was verified.(3)Establishing a grey target decision-making model with monotonic three-parameter interval grey number.Firstly,for the case of monotonically increasing or monotonically decreasing three-parameter interval grey number,the definitions and possibility functions of the two were given respectively.Secondly,the distance measurement formulas of monotonically increasing and monotonically decreasing three-parameter interval grey number were given.Then,the grey target decision-making models with monotonically increasing and monotonically decreasing three-parameter interval grey number were constructed.Finally,the grey target decision-making models with monotonically increasing and monotonically decreasing three-parameter interval grey number were verified by examples respectively.All the above-mentioned models had been verified by examples and numerical examples,which demonstrated the rationality,scientificity and effectiveness of the models.In the distance measure of three-parameter interval grey number,the constructed model considered different shapes of attribute value possibility functions,made full use of the background information in the decision-making process of three-parameter interval grey number,enriched the method system of three-parameter interval grey number decision-making,and provided a new way to solve the problem of three-parameter interval grey number decision-making.