Abstract
To secure the quick response of knowledgeable manufacturing system (KMS) to the dynamic production environment and its desirable adaptability and competitiveness, we propose a matching decision method that is based on the improved support vector machine (ISVM for short), and the production environment. Taking into account the uncertainty and fuzziness of the production environment, the triangular fuzzy numbers are introduced to represent the uncertain input factors. Independent penalty coefficients are employed for different categories to address the problem of unbalanced samples. To meet the requirement for classifying small, uncertain input, and unbalanced samples, an improved SVM model based on triangular fuzzy theory is put forward. Considering the mutagenic factor and dynamic weight, we improve the particle swarm algorithm to optimize the model parameters. The matching categories of KMS and dynamic production environment are defined, and the corresponding matching decision method based on ISVM model is built. Case study shows that the proposed ISVM matching decision method is feasible and effective.
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Abbreviations
 \(\lambda \) :

Confidence level, \(\lambda \in [0,1]\)
 \(\hbox {Pos}\{\cdot \}\) :

Possibility measure of the fuzzy event \(\{\cdot \}\)
 \({\tilde{{\varvec{x}}}}_i\) :

Triangular fuzzy number vector
 \({\tilde{X}}\) :

Fuzzy input set, \({\tilde{X}}=\{{\tilde{{\varvec{x}}}}_1 ,{\tilde{{\varvec{x}}}}_2 ,\ldots ,{\tilde{{\varvec{x}}}}_l \}\)
 y :

Output set, \(y=\{y_1 ,y_2 ,\ldots ,y_l \}\)
 S :

Fuzzy training set, \(S=\{({\tilde{{\varvec{x}}}}_1 ,y_1 ),({\tilde{{\varvec{x}}}}_2 ,y_2 ),\ldots ,({\tilde{{\varvec{x}}}}_l ,y_l )\}\)
 \({\mathbf {\omega }}\) :

Normal vector of the hyper plane
 b :

Offset of the hyper plane
 C :

Penalty coefficient of classification error (\(C>0)\)
 \(C^{+}\) :

Penalty coefficients of positive category (\(C^{+}>0)\)
 \(C^{}\) :

Penalty coefficients of negative category (\(C^{}>0)\)
 \({\varvec{\xi }} \) :

Slack viable
 \(R^{n}\) :

Lowdimensional input space
 H :

Highdimensional feature space
 \(\phi \) :

Transformation of low dimensional space into high dimension space
 \(({\varvec{\beta }}',{\varvec{\alpha }}')'\) :

Decision variable, \({\varvec{\beta }} =(\beta _1 ,\ldots ,\beta _p)',{\varvec{\alpha }} =(\alpha _{p+1} ,\ldots ,\alpha _l )'\)
 \(N_{\mathrm {sv}}\) :

Set of support vector
 \(n_{\mathrm {sv}}\) :

Number of support vector
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Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grants 61673112 and 60934008, the Natural Science Foundation of the Higher Education Institution of Jiangsu Province under Grant 16KJD460005, the Fundamental Research Funds for the Central Universities of China under Grant 2242014K10031 and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). We thank the EditorinChief and Professor Andrew Kusiak, the anonymous reviewers and Professor Li Lu for their valuable comments and suggestions.
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Yan, H., Wang, Y. Matching decision method for knowledgeable manufacturing system and its production environment. J Intell Manuf 30, 771–782 (2019) doi:10.1007/s1084501612831
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Keywords
 Knowledgeable manufacturing system
 Production environment
 Matching classification
 Support vector machine