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Today, Xiaobian brings you the 3. MCDM model based on correlation coefficients of IVIFNs in the intensive reading journal paper "Multi-criteria Decision Model Based on Interval Intuitionistic Fuzzy Number Correlation Coefficient".
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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）
In this issue, we will introduce the MCDM model based on IVIFNs correlation coefficient of the intensive reading journal paper "Multi-criteria Decision Making Model Based on Interval Intuitionistic Fuzzy Number Correlation Coefficient" from three aspects: mind map, intensive reading content, and knowledge supplement.
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）
The multi-criterion decision-making problem discussed in this paper is defined as the selection of the optimal scheme strategy from many alternatives when the evaluation value of each alternative scheme is expressed by an interval intuitionistic fuzzy number, and the weight information of each decision criterion is completely unknown, and the algorithm steps are shown in the figure below.
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.
The specific steps are as follows: Step 1, identify the set of alternatives, The scheme evaluation criterion set and the decision matrix containing the interval intuitionistic fuzzy information;Step 2 determines the ideal scheme and the critical scheme according to the interval intuitionistic fuzzy information decision matrix;Step 3 calculates the correlation coefficient between each alternative scheme and the ideal scheme and the critical scheme;Step 4 determines the weights of each evaluation criterion with the ideal scheme as the reference object and the weight of each evaluation criterion with the critical scheme as the reference object;Step 5 gathers the information of the judgment matrix based on the interval intuitionistic fuzzy correlation coefficient and the weight information of each criterion to obtain the weighted correlation coefficient of the alternative scheme and the ideal scheme;step 6According to the processing of the weighted correlation coefficient of each alternative scheme and the ideal scheme and the critical scheme, the scheme is ranked to obtain the optimal scheme. This is shown in the figure below.
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.
The modeling principle of step 4 is shown in the following figure. The authors eliminate the influence of positive and negative signs on the weight calculation, and the criterion weight vector is chosen to minimize the sum of the total deviations of all alternatives under each criterion. Then, the Lagrangian function is used to obtain the weights of each criterion with the ideal scheme and the critical scheme as the reference objects.
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）
In a mathematical optimal problem, the Lagrangian multiplier method is a method of finding the extreme values of a multivariate function where a variable is limited by one or more conditions. This method transforms an optimization problem with n variables and k constraints into an extreme problem with a system of equations with n + k variables, the variables of which are not constrained in any way. This method introduces a new type of scalar unknown, the Lagrange multiplier: the coefficient of each vector in the linear combination of the gradients of the constraint equation. Its mathematical definition is shown in the figure below.
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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References: ChatGPT, Baidu Encyclopedia
Bibliography:
Yuan Yu, Guan Tao, Yan Xiangbin et al. Multi-criterion Decision Model Based on Correlation Coefficients of Interval Intuitionistic Fuzzy Numbers [J]. Journal of Management Science, 2014, 17(4): 11-18.
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