动态Pythagorean模糊多属性决策的Topsis方法

Topsis Method for Dynamic Pythagorean Fuzzy Multi-attribute Decision Making

针对决策属性信息为Pythagorean模糊数的动态多属性决策问题,提出了一种新的动态多属性决策方法。首先利用Pythagorean模糊熵建立非线性规划模型确定各时段内决策属性的权重;然后运用Pythagorean模糊加权平均(PFWA)算子将各个时段内的决策方案的决策属性进行集结,建立了决策方案关于时段的决策矩阵;最后借助"厚今薄古"思想求解各个时段的时序权重,利用理想解法求解各个决策方案在各个时段的正理想解距离和负理想距离,通过各个决策方案的相对贴进度对决策方案进行排序,通过案例分析说明本文提出方法的有效性。本文的创新和特色,一是各个时段内的决策属性的权重是动态变化的,而不是一成不变的;二是各个时段都有不同的权重,体现了时间变化对决策方案的影响;三是Pythagorean模糊数的距离公式体现了隶属度、非隶属度、强度度和强度方向四个参数,分析发现用四参数定义的距离比目前大部分文献中所提出的距离更符合实际,也克服了相关文献中提出距离存在问题的弊端。

A new dynamic multi-attribute decision making met hod based on Pythagorean fuzzy numberis proposed.First,a nonlinear programming model is established by using Pythagorean fuzzy entropyto determine the weight of decision attributes in each time period.Then using Pythagorean fuzzyweighted average operator to aggregate the decision attributes of the decision scheme in each timeperiod,the decision matrix of the decision scheme in terms of time period is established.Finally.by laying more stress on the present information than on the past to solve the weights the time series,using the ideal method to solve the decision-making plan in each period of time from positive idealsolution and negative ideal distance,through various decision-making plan the relative progress ofdecisior-making scheme for sorting,through case to illustrate the effectiveness of the methodproposed in this paper.The innovation and characteristics of this paper are as follows:firstly,theweight of decision attributes changes dynamically in each period of time,instead of being invariable;Secondly,each time period has different weights,which reflects the influence of time change on thedecision-making scheme.Third,the distance formula of Pythagorean fuzzy number reflects the fourparameters of membership degree μ_(p),non membership degree v_(p),confidence degree r_(p) and direction d_(p),through case analysis,it is found that the distance defined by the four parameters is morepractical than the distance proposed in most current literatures and overcomes the disadvantages of thedistance proposed in relevant literatures.