Choquet integral-based suction resistance multi-attribute coupling influence analysis method

Abstract

The invention specifically discloses a Choquet integral-based suction resistance multi-attribute coupling influence analysis method, which comprises the following steps of: constructing a cigarette data set to form a cigarette attribute detection data set and a suction resistance detection data set; using a Choquet integral as an aggregation model to aggregate the cigarette attribute detection data set and the draw resistance detection data set so as to construct a Choquet integral model between cigarette attributes and draw resistance; according to the Choquet integral model, performing numerical solution on each attribute and the fuzzy measure corresponding to the cigarette draw resistance; and according to a calculation result of the fuzzy measure, solving an interaction index and a generalized Shapley value between the cigarette attributes so as to determine a main attribute index influencing the draw resistance. The accuracy of cigarette draw resistance analysis can be improved, and the production quality of cigarettes is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of cigarette draw resistance, and more specifically, to a draw resistance multi-attribute coupling influence analysis method based on Choquet integration. Background Art

[0002] In recent years, as consumers' requirements for cigarette quality have gradually increased, major tobacco companies have also paid more and more attention to improving the quality of cigarette products. As an important physical indicator for testing the quality of cigarette products and for consumers to intuitively feel the characteristics of cigarettes during the smoking process, the stability of cigarette draw resistance not only has a significant impact on the release of smoke chemical indicators, but also has a great impact on the sensory quality of cigarettes such as cigarette smoke volume, irritation, and aroma. However, due to the many factors that affect cigarette draw resistance, the draw resistance of cigarette products is difficult to control. Therefore, it is of great significance to clarify the influence mechanism of each factor on cigarette draw resistance for cigarette process quality control. There are many research methods used to analyze the factors affecting cigarette draw resistance. At present, experimental and mathematical statistics methods are often used to analyze the influence of other indicators on cigarette draw resistance, such as correlation analysis, regression analysis, and multivariate analysis of cigarette draw resistance and other indicators. In addition, the factors affecting draw resistance are analyzed by establishing a cigarette mechanism model for fluid simulation. However, existing methods only focus on the effect of a single indicator attribute on draw resistance, such as length and draw resistance, mass and draw resistance, etc., without considering the reinforcing effect of the coupling between multiple attributes on the draw resistance, which is inconsistent with the actual situation. Although a single indicator attribute itself has little effect on draw resistance, its coupling with other attributes may significantly enhance the impact on draw resistance, resulting in a "1+1 greater than 2" effect. Existing research methods do not have the ability to analyze the effect of such coupling between attributes on draw resistance. Therefore, it is of great significance to explore the effect of the coupling between the attributes of cigarettes on draw resistance, find the attribute combination with a significant reinforcing effect, and determine the main attribute indicators that affect draw resistance. Summary of the invention

[0003] The present invention provides a method for analyzing the multi-attribute coupling influence of draw resistance based on Choquet integral, which solves the problem that the existing draw resistance analysis of cigarettes only focuses on the influence of the draw resistance of a single index attribute and the draw resistance analysis is inaccurate, and can improve the accuracy of the draw resistance analysis of cigarettes and improve the production quality of cigarettes.

[0004] To achieve the above objectives, the present invention provides the following technical solutions:

[0005] A method for analyzing the multi-attribute coupling effects of absorption and resistance based on Choquet integral, including:

[0006] Constructing a cigarette dataset to form a cigarette attribute detection dataset and a draw resistance detection dataset;

[0007] Using Choquet integral as an aggregation model, aggregating the cigarette attribute detection dataset and the draw resistance detection dataset to construct a Choquet integral model between cigarette attributes and draw resistance;

[0008] Numerically solving the fuzzy measures corresponding to each attribute and the cigarette draw resistance according to the Choquet integral model;

[0009] The interaction index and generalized Shapley value between the attributes of each cigarette are solved according to the calculation result of the fuzzy measurement to determine the main attribute index affecting the draw resistance.

[0010] Preferably, the constructing of the cigarette dataset comprises:

[0011] The collected cigarette data is composed of The form matrix, where For the The first properties, For the Resistance to draw of cigarette carton data.

[0012] Preferably, the construction of a Choquet integral model between cigarette attributes and draw resistance includes:

[0013] The decision matrix including the cigarette attribute detection data set and the draw resistance detection data set is represented by a matrix P;

[0014] Perform Choquet integration between cigarette properties and draw resistance;

[0015] Construct the objective function and inequality constraints for cigarette attributes.

[0016] Preferably, the numerically solving the fuzzy measure corresponding to each attribute and the cigarette draw resistance according to the Choquet integral model includes:

[0017] The cigarette attribute data of the decision matrix are aggregated to obtain an aggregate value of each cigarette attribute, and the fuzzy measure is identified by minimizing the error term between the aggregate value and the draw resistance detection value.

[0018] Preferably, identifying the fuzzy measure by minimizing the error term between the aggregate value and the draw resistance detection value comprises:

[0019] The fuzzy measure is identified by minimizing the quadratic error term, as follows: ,in, is the aggregation value, and m is the number of cigarettes.

[0020] Preferably, identifying the fuzzy measure by minimizing the quadratic error term comprises:

[0021] The Choquet integral of the objective function with respect to a fuzzy measure is expressed as the vector multiplication of the Möbius transform of the fuzzy measure and the input vector;

[0022] The fuzzy measure of cigarette attributes is identified by obtaining the Möbius transform of the fuzzy measure of cigarette attributes.

[0023] Preferably, the Choquet integral includes:

[0024] According to the formula: , calculated The Choquet integral of , , , To influence the draw resistance of cigarettes Item attributes, is the fuzzy measure of cigarette attributes Möbius transform.

[0025] Preferably, the objective function and inequality constraints for constructing cigarette attributes include:

[0026] The error of the attribute data of the jth cigarette is: , then the objective function or estimation error is expressed as: ;

[0027] The inequality constraints are: for all , all satisfied , where A and B are both sets of cigarette attributes.

[0028] Preferably, solving the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation result of the fuzzy measure includes:

[0029] The definition of the interaction index of the fuzzy measure μ is:

[0030]

[0031] Among them, A is the attribute set of cigarettes, Cigarette properties Cigarette properties The interaction index of

[0032] when When the value is 1, it means that the effects of the two groups of cigarette attributes on draw resistance are maximally complementary;

[0033] when When the value is -1, it means that the effects of the two groups of cigarette attributes on draw resistance are maximally redundant.

[0034] Preferably, solving the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation result of the fuzzy measure includes:

[0035] According to the formula , where S, Ω, and T are the attribute sets of each cigarette, and s, n, and t represent the potential indexes corresponding to S, Ω, and T respectively. is the Shapley value of the effect of cigarette attribute set S on draw resistance.

[0036] The present invention provides a method for analyzing the multi-attribute coupling influence of draw resistance based on Choquet integral. By constructing a cigarette data set and a Choquet integral model and performing fuzzy measurement solution, the main attribute index affecting the draw resistance is obtained, so as to solve the problem that the existing cigarette draw resistance analysis only focuses on the influence of a single indicator attribute on the draw resistance, resulting in inaccurate draw resistance analysis. The method can improve the accuracy of cigarette draw resistance analysis and improve the production quality of cigarettes. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the specific embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below.

[0038] Figure 1 It is a schematic diagram of a method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral provided by the present invention.

[0039] Figure 2 It is a flowchart of the steps of constructing a Choquet integral model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to enable persons skilled in the art to better understand the solutions of the embodiments of the present invention, the embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and implementation modes.

[0041] In view of the problem that the current cigarette draw resistance analysis does not accurately determine the attribute index that affects the draw resistance, the present invention provides a draw resistance multi-attribute coupling influence analysis method based on Choquet integral, which solves the problem that the existing cigarette draw resistance analysis only focuses on the influence of a single indicator attribute on the draw resistance, resulting in inaccurate draw resistance analysis, and can improve the accuracy of cigarette draw resistance analysis and improve the production quality of cigarettes.

[0042] like Figure 1 As shown, a method for analyzing the multi-attribute coupling influence of absorption and resistance based on Choquet integral includes:

[0043] S1: Construct a cigarette dataset to form a cigarette attribute detection dataset and a draw resistance detection dataset.

[0044] S2: Using Choquet integral as an aggregation model, the cigarette attribute detection dataset and the draw resistance detection dataset are aggregated to construct a Choquet integral model between cigarette attributes and draw resistance.

[0045] S3: According to the Choquet integral model, the fuzzy measure corresponding to each attribute and the cigarette draw resistance is numerically solved.

[0046] S4: Solve the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation results of the fuzzy measurement to determine the main attribute indicators that affect the draw resistance.

[0047] Specifically, in order to accurately determine the factors that affect the draw resistance of cigarettes, the Choquet integral in fuzzy mathematics is introduced, and the fuzzy measurement is used to explore the coupling effect of attributes that affect the draw resistance of cigarettes. The specific process is: build a cigarette database, build a Choquet integral model between cigarette attributes and draw resistance, use a data-driven method to numerically solve the fuzzy measure in the integral, and then further calculate the interaction index and generalized Shapley value based on the fuzzy measure to determine the main attribute indicators that affect the draw resistance. In this way, the influence of the coupling effect between the various attributes of cigarettes on the draw resistance is explored, the attribute combination with a significant reinforcement effect is found, and the main attribute indicators that affect the draw resistance are determined.

[0048] Furthermore, the cigarette data set construction includes: forming the collected cigarette data into The form matrix, where For the The first properties, For the Resistance to draw of cigarette carton data.

[0049] Furthermore, the construction of the Choquet integral model between cigarette attributes and draw resistance includes:

[0050] The decision matrix including the cigarette attribute detection data set and the draw resistance detection data set is represented by a matrix P;

[0051] Perform Choquet integration between cigarette properties and draw resistance;

[0052] Construct the objective function and inequality constraints for cigarette attributes.

[0053] like Figure 2 As shown, we first use Choquet integration as the aggregation model to The cigarette attribute data is aggregated. An error term is generated between the aggregated value and the draw resistance detection value, and then the fuzzy measure of cigarette attribute is identified by minimizing the error term. The definition of identifying the fuzzy measure by minimizing the quadratic error term is as follows:

[0054] ,in, is the aggregation value, and m is the number of cigarettes.

[0055] In addition to the error, in order to learn the fuzzy measure from the data, we need to pay attention to some constraints related to the fuzzy measure. That is, the set function being searched needs to satisfy the constraints of the fuzzy measure. According to the method described by Imai et al., minimizing the quadratic error term can be regarded as a quadratic optimization problem. Since the constraints related to the fuzzy measure are linear constraints, for a suitable matrix ,vector and matrix , the optimization problem can be viewed as follows:

[0056] ,

[0057] In other words, solving the fuzzy measure of each cigarette attribute can be expressed as a quadratic optimization problem that satisfies linear constraints. Since the Choquet integral is essentially just a linear combination, in order to facilitate the identification of fuzzy measures, the Choquet integral of a function on a measure can be expressed as the vector multiplication established by the Möbius transform of the measure and the input vector. This causes the objective function to become a quadratic expression of matrix multiplication, and the optimization problem also becomes finding the Möbius transform of the fuzzy measure of cigarette attributes, rather than finding the fuzzy measure of cigarette attributes itself.

[0058] Let X be the cigarette dataset used in the process of learning fuzzy measurement, corresponding to Cigarette carton attribute data. Indicates Cigarette carton attribute data. Each piece of data contains Cigarette attributes. is the draw resistance detection data set corresponding to each cigarette attribute detection data. We use the matrix represents the decision matrix containing the cigarette attribute detection dataset and the draw resistance detection dataset, where . Then we can get the matrix Identify cigarette attributes using fuzzy measurement.

[0059] because Is a The input vector of values, let the function in ,but The Choquet integral can be expressed as vector representation, which is called Therefore, for any , The values ​​represented are: .

[0060] pass The Choquet integral can be obtained by linearly multiplying it with the Möbius transform of the fuzzy measure. To express The Möbius transform of the fuzzy measure of all subsets (except the empty set) of . Specifically, given the attribute data of the j-th cigarette ,if Is with data The relevant vector can be used to measure the cigarette attribute fuzzy Möbius transformation calculate The Choquet integral of is as follows: , that is, the Choquet integral can be expressed as the product of two vectors.

[0061] To achieve the objective function, the error of the attribute data of the jth cigarette is as follows: ;

[0062] It can be expressed in matrix form as: ;

[0063] Then the objective function or estimation error can be expressed as: .

[0064] The above expression has the form: ;

[0065] in The effect is equivalent to ,therefore, .

[0066] For inequality constraints, since the fuzzy measure is monotonic, for all , all satisfied For the Möbius transform of fuzzy measure, this condition can also be established equivalently. From the perspective of optimization, it is not necessary to consider that all cigarette attribute sets A and B satisfy . It is only necessary to make the cigarette attribute set A and the cigarette attribute set B have only one element different, such as .

[0067] Given a cigarette attribute set , assuming that the fuzzy measure of the cigarette attribute set is zero or positive. Therefore, when the Möbius transformation hour, ).Right now:

[0068]

[0069] Further, solving the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation result of the fuzzy measure includes:

[0070] The definition of the interaction index of the fuzzy measure μ is:

[0071]

[0072] Among them, the number of cigarette attributes is a set of attributes, Cigarette properties Cigarette properties The interaction index.

[0073] The interaction index can reflect the interaction effect between the two groups of cigarette attributes on the draw resistance. When the value is 1, it means that the effects of the two groups of cigarette attributes on the draw resistance are the most complementary. When the value is -1, it means that the two groups of cigarette attributes have the greatest redundancy in their effects on draw resistance. The larger it is, the stronger the complementarity of the two attributes in affecting the draw resistance is; The smaller it is, the stronger the correlation between the two properties on the absorption resistance is.

[0074] The Shapley function is one of the most important profit indicators in cooperative games. It satisfies the famous validity axiom, symmetry axiom and additivity axiom.

[0075] Further, solving the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation result of the fuzzy measure includes:

[0076] According to the formula:

[0077] Among them, μ is the fuzzy measure on the cigarette attribute set Ω, S, Ω, and T are all sets of cigarette attributes, and s, n, and t represent the potential indicators corresponding to S, Ω, and T respectively. Can be considered as a set of cigarette attributes The weighted average of the marginal contribution to the draw resistance can be used as the global importance of the effect of cigarette attributes on the draw resistance. And the above formula satisfies, ,have and , so It can be used as the final influence weight of each cigarette attribute on draw resistance.

[0078] In one embodiment, physical index test data of 2529 cigarettes of a certain brand are selected for draw resistance analysis:

[0079] Step 1: Construct a cigarette dataset P = [ventilation rate, hardness, circumference, mass, length | draw resistance].

[0080] Step 2: By constructing a Choquet integral model between cigarette attributes and draw resistance, the fuzzy measurements of various attributes are solved from the cigarette data set. The calculation results are shown in Table 1, which are the fuzzy measurements of various attributes of a certain brand of cigarettes.

[0081]

[0082] Step 3: Calculate the interaction index of each attribute through fuzzy measurement calculation results. The calculation results are shown in Table 2, which are the interaction indexes of various attributes of a certain brand of cigarettes.

[0083]

[0084] Step 4: Calculate the generalized Shapley value of each attribute through the fuzzy measurement calculation results. The calculation results are shown in Table 3, which are the generalized Shapley values ​​of each attribute of a certain brand of cigarettes.

[0085]

[0086] From the above table, we can see that the Choquet integral in fuzzy mathematics is introduced to model the coupling effect between attributes that affect the draw resistance of cigarettes, which can analyze the effect of the coupling effect between cigarette attributes on the draw resistance, and obtain the interactive attributes of the influence of various attributes on the draw resistance, so as to find out the attribute combination with a significant strengthening effect on the draw resistance of cigarettes, get rid of the dependence on the experience of experts in the field, and the result is more objective and effective. At the same time, the generalized Shapley value of each attribute is further calculated through the calculated fuzzy measurement results of each attribute, and the weight of the influence of each attribute index on the draw resistance and the global importance of the influence of its combination on the draw resistance can be obtained, so as to determine the main attribute index and its combination that affect the draw resistance of cigarettes.

[0087] It can be seen that the present invention provides a multi-attribute coupling influence analysis method of draw resistance based on Choquet integral, which constructs a cigarette data set and a Choquet integral model, and performs fuzzy measurement to obtain the main attribute indicators that affect the draw resistance, thereby solving the problem that the existing cigarette draw resistance analysis only focuses on the influence of a single indicator attribute on the draw resistance, resulting in inaccurate draw resistance analysis. The method can improve the accuracy of cigarette draw resistance analysis and improve the production quality of cigarettes.

[0088] The above describes in detail the structure, features and effects of the present invention based on the embodiments shown in the drawings. The above is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the drawings. Any changes made in accordance with the concept of the present invention, or modifications to equivalent embodiments with equivalent changes, which still do not exceed the spirit covered by the description and drawings, should be within the protection scope of the present invention.

Claims

1. A method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral, characterized in that: include: Constructing a cigarette dataset to form a cigarette attribute detection dataset and a draw resistance detection dataset; Using Choquet integral as an aggregation model, aggregating the cigarette attribute detection dataset and the draw resistance detection dataset to construct a Choquet integral model between cigarette attributes and draw resistance; Numerically solving the fuzzy measures corresponding to each attribute and the cigarette draw resistance according to the Choquet integral model; The interaction index and generalized Shapley value between the attributes of each cigarette are solved according to the calculation result of the fuzzy measurement to determine the main attribute index affecting the draw resistance.

2. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 1, characterized in that: The step of constructing a cigarette dataset comprises: The collected cigarette data is composed of The form matrix, where For the The first properties, For the Resistance to draw of cigarette carton data.

3. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 2, characterized in that: The method of constructing a Choquet integral model between cigarette attributes and draw resistance includes: The decision matrix including the cigarette attribute detection data set and the draw resistance detection data set is represented by a matrix P; Perform Choquet integration between cigarette properties and draw resistance; Construct the objective function and inequality constraints for cigarette attributes.

4. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 3, characterized in that: The method of numerically solving the fuzzy measure corresponding to each attribute and the cigarette draw resistance according to the Choquet integral model includes: The cigarette attribute data of the decision matrix are aggregated to obtain an aggregate value of each cigarette attribute, and the fuzzy measure is identified by minimizing the error term between the aggregate value and the draw resistance detection value.

5. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 4, characterized in that: The identifying the fuzzy measure by minimizing the error term between the aggregate value and the draw resistance detection value comprises: The fuzzy measure is identified by minimizing the quadratic error term, as follows: ,in, is the aggregation value, and m is the number of cigarettes.

6. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 5, characterized in that: The method of identifying the fuzzy measure by minimizing the quadratic error term includes: The Choquet integral of the objective function with respect to a fuzzy measure is expressed as the vector multiplication of the Möbius transform of the fuzzy measure and the input vector; The fuzzy measure of cigarette attributes is identified by obtaining the Möbius transform of the fuzzy measure of cigarette attributes.

7. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 6, characterized in that: The Choquet integral includes: According to the formula: , calculated The Choquet integral of , , , To influence the draw resistance of cigarettes Item attributes, is the fuzzy measure of cigarette attributes Möbius transform.

8. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 7, characterized in that: The objective function and inequality constraints for constructing cigarette attributes include: The error of the attribute data of the jth cigarette is: , then the objective function or estimation error is expressed as: ; The inequality constraints are: for all , all satisfied , where A and B are both sets of cigarette attributes.

9. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 8, characterized in that: Solving the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation result of the fuzzy measure includes: The definition of the interaction index of the fuzzy measure μ is: Among them, A is the attribute set of cigarettes, Cigarette properties Cigarette properties The interaction index of when When the value is 1, it means that the effects of the two groups of cigarette attributes on draw resistance are maximally complementary; when When the value is -1, it means that the effects of the two groups of cigarette attributes on draw resistance are maximally redundant.

10. The method for analyzing the multi-attribute coupling influence of absorption resistance based on Choquet integral according to claim 9, characterized in that: Solving the interaction index and generalized Shapley value between the attributes of each cigarette according to the calculation result of the fuzzy measure includes: According to the formula , where S, Ω, and T are the attribute sets of each cigarette, and s, n, and t represent the potential indexes corresponding to S, Ω, and T, respectively. is the Shapley value of the effect of cigarette attribute set S on draw resistance.

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