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今天小编为您带来精读期刊论文《基于区间直觉模糊数相关系数的多准则决策模型》的3.基于IVIFNs相关系数的MCDM模型。
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Today, the editor brings the "3. MCDM model based on IVIFNs correlation coefficient of the journal paper 'Multi-criterion decision model based on interval-intuitionistic fuzzy number correlation coefficient'".
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一、内容摘要（Content summary）
本期推文将从思维导图、精读内容、知识补充三个方面介绍精读期刊论文《基于区间直觉模糊数相关系数的多准则决策模型》的3.基于IVIFNs相关系数的MCDM模型。
In this issue, the tweet will introduce the e "3. MCDM model based on IVIFNs correlation coefficient of the journal paper "Multi-criteria Decision Model Based on Interval Intuitionistic Fuzzy Number Correlation Coefficient" from three aspects: mind map, detailed reading content, and additional knowledge supplementation.
二、思维导图（Mind Mapping）
三、精读内容（Detailed Reading Content）
本文探讨的多准则决策问题界定为各备选方案评价值以区间直觉模糊数表达，且各决策准则的权重信息完全未知情况下，从众多备选方案中选择最优方案策略，其算法步骤如下图所示。
The multi-criteria decision-making problem discussed in this paper is defined as the evaluation of alternative solutions expressed as interval intuitionistic fuzzy numbers, with the weights of each decision criterion being completely unknown. The algorithmic steps for selecting the optimal solution strategy from numerous alternatives are as follows.
具体步骤如下：步骤1，确定备选方案集合、方案评价准则集合以及含有区间直觉模糊信息的决策矩阵；步骤2，依据区间直觉模糊信息决策矩阵确定理想方案和临界方案；步骤3，计算各备选方案与理想方案及临界方案的相关系数；步骤4，确定以理想方案为参照对象的各评价准则权重，以及以临界方案为参照对象的各评价准则权重；步骤5，将基于区间直觉模糊相关系数判断矩阵与各准则权重信息集结，得到备选方案与理想方案的加权相关系数；步骤6，根据各备选方案与理想方案和临界方案的加权相关系数的处理，从而进行方案排序，得到最优方案。如下图所示。
Specific steps are as follows: Step 1, determine the set of alternative solutions, the set of evaluation criteria for solutions, and the decision matrix containing interval intuitionistic fuzzy information; Step 2, based on the decision matrix with interval intuitionistic fuzzy information, determine the ideal solution and the critical solution; Step 3, calculate the correlation coefficients between each alternative solution and the ideal solution and critical solution; Step 4, determine the weights of evaluation criteria with the ideal solution as the reference object, and the weights of evaluation criteria with the critical solution as the reference object; Step 5, consolidate the judgment matrix based on interval intuitionistic fuzzy correlation coefficients and the information of each criterion weight, to obtain the weighted correlation coefficients between alternative solutions and the ideal solution; Step 6, based on the processing of weighted correlation coefficients between each alternative solution and the ideal solution and critical solution, rank the solutions to obtain the optimal solution. As shown in the figure below.
其中，步骤4的建模原理如下图所示。作者消除了正负号对权重计算的影响，准则权重向量的选择使各准则下所有备选方案的总偏差之和最小。然后，运用拉格朗日函数，得到以理想方案和临界方案为参照对象的各准则权重计算公式。
The modeling principle of Step 4 is shown in the figure below. The author eliminates the influence of positive and negative signs on weight calculation, and selects the criterion weight vector to minimize the total deviation of all alternative solutions under each criterion. Then, by using the Lagrange function, the formulas for calculating the weights of each criterion with the ideal solution and critical solution as the reference objects are obtained.
四、知识补充——拉格朗日乘数法（Supplementary Knowledge —— Lagrange Multiplier Method）
在数学最优问题中，拉格朗日乘数法是一种寻找变量受一个或多个条件所限制的多元函数的极值的方法。这种方法将一个有n个变量与k个约束条件的最优化问题转换为一个有n+k个变量的方程组的极值问题，其变量不受任何约束。这种方法引入了一种新的标量未知数，即拉格朗日乘数：约束方程的梯度的线性组合里每个向量的系数。其数学定义如下图所示。
In mathematical optimization problems, the Lagrange multiplier method is a method for finding the extremum of a multivariate function subject to one or more constraints. This method transforms an optimization problem with n variables and k constraints into an extremum problem of a system of equations with n+k variables, where the variables are not subject to any constraints. This method introduces a new scalar unknown, namely the Lagrange multiplier: the coefficients of each vector in the linear combination of the gradients of the constraint equations. Its mathematical definition is shown in the figure below.
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参考资料：ChatGPT、百度百科
参考文献：
袁宇, 关涛, 闫相斌等. 基于区间直觉模糊数相关系数的多准则决策模型 [J]. 管理科学学报, 2014, 17(4): 11-18.
本文由LearningYard学苑整理并发出，如有侵权请在后台留言！
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