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今天小編為您帶來精讀期刊論文《基于區間直覺模糊數相關系數的多準則決策模型》的3.基于IVIFNs相關系數的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）
本期推文将從思維導圖、精讀内容、知識補充三個方面介紹精讀期刊論文《基于區間直覺模糊數相關系數的多準則決策模型》的3.基于IVIFNs相關系數的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、思維導圖（Mind Mapping）
三、精讀内容（Detailed Reading Content）
本文探讨的多準則決策問題界定為各備選方案評價值以區間直覺模糊數表達，且各決策準則的權重資訊完全未知情況下，從衆多備選方案中選擇最優方案政策，其算法步驟如下圖所示。
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.
具體步驟如下：步驟1，确定備選方案集合、方案評價準則集合以及含有區間直覺模糊資訊的決策矩陣；步驟2，依據區間直覺模糊資訊決策矩陣确定理想方案和臨界方案；步驟3，計算各備選方案與理想方案及臨界方案的相關系數；步驟4，确定以理想方案為參照對象的各評價準則權重，以及以臨界方案為參照對象的各評價準則權重；步驟5，将基于區間直覺模糊相關系數判斷矩陣與各準則權重資訊集結，得到備選方案與理想方案的權重相關系數；步驟6，根據各備選方案與理想方案和臨界方案的權重相關系數的處理，進而進行方案排序，得到最優方案。如下圖所示。
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，步驟4的模組化原理如下圖所示。作者消除了正負号對權重計算的影響，準則權重向量的選擇使各準則下所有備選方案的總偏差之和最小。然後，運用拉格朗日函數，得到以理想方案和臨界方案為參照對象的各準則權重計算公式。
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、知識補充——拉格朗日乘數法（Supplementary Knowledge —— Lagrange Multiplier Method）
在數學最優問題中，拉格朗日乘數法是一種尋找變量受一個或多個條件所限制的多元函數的極值的方法。這種方法将一個有n個變量與k個限制條件的最優化問題轉換為一個有n+k個變量的方程組的極值問題，其變量不受任何限制。這種方法引入了一種新的标量未知數，即拉格朗日乘數：限制方程的梯度的線性組合裡每個向量的系數。其數學定義如下圖所示。
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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參考資料：ChatGPT、百度百科
參考文獻：
袁宇, 關濤, 闫相斌等. 基于區間直覺模糊數相關系數的多準則決策模型 [J]. 管理科學學報, 2014, 17(4): 11-18.
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