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Erschienen in: Soft Computing 13/2023

07.01.2023 | Application of soft computing

A novel granular variable precision fuzzy rough set model and its application in fuzzy decision system

verfasst von: Dan-Dan Zou, Yao-Liang Xu, Ling-Qiang Li, Wei-Zhi Wu

Erschienen in: Soft Computing | Ausgabe 13/2023

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Abstract

The comparable property (or inclusion property) is the basic property of rough set theory. Unfortunately, the well-known granular variable precision fuzzy rough set does not satisfy the comparable property. To remedy this gap, a novel granular variable precision fuzzy rough set model with comparable property is proposed and discussed. Firstly, by analyzing the existing granular precision fuzzy rough set models, we find the reason that they do not satisfy the comparable property. Then, we give a new granular precision fuzzy rough set model with the comparable property. Secondly, we study the basic properties, characterization theorem and accuracy measure of the new model. Thirdly, we apply the novel model in the study of fuzzy decision system. An attribute reduction method is developed, and the corresponding attribute reduction algorithm is designed. Finally, by using public accessible datasets, we make a series of experiments to verify the effectiveness and reliability of our method and make comparisons with some existing attribute reduction methods.

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Literatur
Zurück zum Zitat Al-shami TM (2021) An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application. Inf Sci 569:110–124MathSciNet Al-shami TM (2021) An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application. Inf Sci 569:110–124MathSciNet
Zurück zum Zitat Baczynski M, Jayaram B (2008) Fuzzy implications. Springer, BerlinMATH Baczynski M, Jayaram B (2008) Fuzzy implications. Springer, BerlinMATH
Zurück zum Zitat Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in the rough set theory. Inf Sci 107(1–4):149–167MathSciNetMATH Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in the rough set theory. Inf Sci 107(1–4):149–167MathSciNetMATH
Zurück zum Zitat Chen DG, Yang YP, Wang H (2011) Granular computing based on fuzzy similarity relations. Soft Comp 15(6):1161–1172MATH Chen DG, Yang YP, Wang H (2011) Granular computing based on fuzzy similarity relations. Soft Comp 15(6):1161–1172MATH
Zurück zum Zitat Cornelis C, Cock MD, Radzikowska AM (2007) Vaguely quantified rough sets. In International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing (pp. 87–94). Springer, Berlin & Heidelberg Cornelis C, Cock MD, Radzikowska AM (2007) Vaguely quantified rough sets. In International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing (pp. 87–94). Springer, Berlin & Heidelberg
Zurück zum Zitat Csajbók ZE, Mihálydeák T (2014) From vagueness to rough sets in partial approximation spaces. In Rough Sets and Intelligent Systems Paradigms (pp. 42–52). Springer, Cham Csajbók ZE, Mihálydeák T (2014) From vagueness to rough sets in partial approximation spaces. In Rough Sets and Intelligent Systems Paradigms (pp. 42–52). Springer, Cham
Zurück zum Zitat Dai JH, Zou XT, Wu WZ (2022) Novel fuzzy \(\beta \)-covering rough set models and their applications. Inf Sci 608:286–312 Dai JH, Zou XT, Wu WZ (2022) Novel fuzzy \(\beta \)-covering rough set models and their applications. Inf Sci 608:286–312
Zurück zum Zitat D’eer L, Verbiest N, Cornelis C, Godo L (2015) A comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis. Fuzzy Sets Sys 275:1–38MathSciNetMATH D’eer L, Verbiest N, Cornelis C, Godo L (2015) A comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis. Fuzzy Sets Sys 275:1–38MathSciNetMATH
Zurück zum Zitat Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J General Sys 17(2–3):191–209MATH Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J General Sys 17(2–3):191–209MATH
Zurück zum Zitat Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J General Sys 17(2–3):191–209MATH Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J General Sys 17(2–3):191–209MATH
Zurück zum Zitat Fang BW, Hu BQ (2019) Granular fuzzy rough sets based on fuzzy implicators and coimplicators. Fuzzy Sets Sys 359:112–139MathSciNetMATH Fang BW, Hu BQ (2019) Granular fuzzy rough sets based on fuzzy implicators and coimplicators. Fuzzy Sets Sys 359:112–139MathSciNetMATH
Zurück zum Zitat Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Sys 17(2):153–171MATH Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Sys 17(2):153–171MATH
Zurück zum Zitat Hassanien AE (2007) Fuzzy rough sets hybrid scheme for breast cancer detection. Image Vis Comp 25(2):172–183 Hassanien AE (2007) Fuzzy rough sets hybrid scheme for breast cancer detection. Image Vis Comp 25(2):172–183
Zurück zum Zitat Hu Q, Xie Z, Yu D (2007) Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Patt Recogn 40(12):3509–3521MATH Hu Q, Xie Z, Yu D (2007) Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Patt Recogn 40(12):3509–3521MATH
Zurück zum Zitat Hu QH, Zhang L, An S, Zhang D (2012) On robust fuzzy rough set models. IEEE Trans Fuzzy Sys 20(4):636–651 Hu QH, Zhang L, An S, Zhang D (2012) On robust fuzzy rough set models. IEEE Trans Fuzzy Sys 20(4):636–651
Zurück zum Zitat Huang ZH, Li JJ (2022) Discernibility measures for fuzzy \(\beta \)-covering and their application. IEEE Trans Cybern 52(9):9722–9735 Huang ZH, Li JJ (2022) Discernibility measures for fuzzy \(\beta \)-covering and their application. IEEE Trans Cybern 52(9):9722–9735
Zurück zum Zitat Jensen R, Shen Q (2007) Fuzzy-rough sets assisted attribute selection. IEEE Trans Fuzzy Sys 15(1):73–89 Jensen R, Shen Q (2007) Fuzzy-rough sets assisted attribute selection. IEEE Trans Fuzzy Sys 15(1):73–89
Zurück zum Zitat Jensen R, Shen Q (2008) New approaches to fuzzy-rough feature selection. IEEE Trans Fuzzy Sys 17(4):824–838 Jensen R, Shen Q (2008) New approaches to fuzzy-rough feature selection. IEEE Trans Fuzzy Sys 17(4):824–838
Zurück zum Zitat Jiang HB, Zhan JM, Chen DG (2018) Covering based variable precision \(({\cal{I} }, {\cal{T} })\)-fuzzy rough sets with applications to multiattribute decision-making. IEEE Trans Fuzzy Sys 27(8):1558–1572 Jiang HB, Zhan JM, Chen DG (2018) Covering based variable precision \(({\cal{I} }, {\cal{T} })\)-fuzzy rough sets with applications to multiattribute decision-making. IEEE Trans Fuzzy Sys 27(8):1558–1572
Zurück zum Zitat Jiang HB, Zhan JM, Chen DG (2021) Covering-based variable precision \(L\)-fuzzy rough sets based on residuated lattices and corresponding applications. Int J Mach Learn Cybern 12(8):2407–2429 Jiang HB, Zhan JM, Chen DG (2021) Covering-based variable precision \(L\)-fuzzy rough sets based on residuated lattices and corresponding applications. Int J Mach Learn Cybern 12(8):2407–2429
Zurück zum Zitat Klement EP, Mesiar R, Pap E (2000) Triangular Norms. Trends in Logic. Kluwer Academic Publishers, DordrechtMATH Klement EP, Mesiar R, Pap E (2000) Triangular Norms. Trends in Logic. Kluwer Academic Publishers, DordrechtMATH
Zurück zum Zitat Li LQ, Jin Q, Hu K, Zhao FF (2017) The axiomatic characterizations on \(L\)-fuzzy covering-based approximation operators. Int J General Sys 46(4):332–353MathSciNet Li LQ, Jin Q, Hu K, Zhao FF (2017) The axiomatic characterizations on \(L\)-fuzzy covering-based approximation operators. Int J General Sys 46(4):332–353MathSciNet
Zurück zum Zitat Li LQ, Jin Q, Yao BX, Wu JC (2020) A rough set model based on fuzzifying neighborhood systems. Soft Comp 24(8):6085–6099MATH Li LQ, Jin Q, Yao BX, Wu JC (2020) A rough set model based on fuzzifying neighborhood systems. Soft Comp 24(8):6085–6099MATH
Zurück zum Zitat Li LQ, Yao BX, Zhan JM, Jin Q (2021) \(L\)-fuzzifying approximation operators derived from general \(L\)-fuzzifying neighborhood systems. Int J Mach Learn Cybern 12(5):1343–1367 Li LQ, Yao BX, Zhan JM, Jin Q (2021) \(L\)-fuzzifying approximation operators derived from general \(L\)-fuzzifying neighborhood systems. Int J Mach Learn Cybern 12(5):1343–1367
Zurück zum Zitat Liu M, Chen DG, Wu C, Li HX (2006) Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems. Comp Math Appl 51(9–10):1507–1518MathSciNetMATH Liu M, Chen DG, Wu C, Li HX (2006) Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems. Comp Math Appl 51(9–10):1507–1518MathSciNetMATH
Zurück zum Zitat Ma LW (2016) Two fuzzy covering rough set models and their generalizations over fuzzy lattices. Fuzzy Sets Sys 294:1–17MathSciNetMATH Ma LW (2016) Two fuzzy covering rough set models and their generalizations over fuzzy lattices. Fuzzy Sets Sys 294:1–17MathSciNetMATH
Zurück zum Zitat Ma MH, Chakraborty MK (2016) Covering-based rough sets and modal logics. Part I. Int J Appr Reason 77:55–65MathSciNetMATH Ma MH, Chakraborty MK (2016) Covering-based rough sets and modal logics. Part I. Int J Appr Reason 77:55–65MathSciNetMATH
Zurück zum Zitat Mi JS, Zhang WX (2004) An axiomatic characterization of a fuzzy generalization of rough sets. Inf Sci 160(1–4):235–249MathSciNetMATH Mi JS, Zhang WX (2004) An axiomatic characterization of a fuzzy generalization of rough sets. Inf Sci 160(1–4):235–249MathSciNetMATH
Zurück zum Zitat Mi JS, Leung Y, Zhao HY, Feng T (2008) Generalized fuzzy rough sets determined by a triangular norm. Inf Sci 178(16):3203–3213MathSciNetMATH Mi JS, Leung Y, Zhao HY, Feng T (2008) Generalized fuzzy rough sets determined by a triangular norm. Inf Sci 178(16):3203–3213MathSciNetMATH
Zurück zum Zitat Mieszkowicz-Rolka A, Rolka L (2004) Variable precision fuzzy rough sets. Transactions on rough sets I. Springer, Berlin & Heidelberg, pp 144–160MATH Mieszkowicz-Rolka A, Rolka L (2004) Variable precision fuzzy rough sets. Transactions on rough sets I. Springer, Berlin & Heidelberg, pp 144–160MATH
Zurück zum Zitat Morsi NN, Yakout MM (1998) Axiomatics for fuzzy rough sets. Fuzzy Sets Sys 100(1–3):327–342MathSciNetMATH Morsi NN, Yakout MM (1998) Axiomatics for fuzzy rough sets. Fuzzy Sets Sys 100(1–3):327–342MathSciNetMATH
Zurück zum Zitat Pang B, Mi JS, Yao W (2019) \(L\)-fuzzy rough approximation operators via three new types of \(L\)-fuzzy relations. Soft Comp 23:11433–11446MATH Pang B, Mi JS, Yao W (2019) \(L\)-fuzzy rough approximation operators via three new types of \(L\)-fuzzy relations. Soft Comp 23:11433–11446MATH
Zurück zum Zitat Pawlak Z (1982) Rough sets. Int J Comp Inf Sci 11(5):341–356MATH Pawlak Z (1982) Rough sets. Int J Comp Inf Sci 11(5):341–356MATH
Zurück zum Zitat Qiao JS, Hu BQ (2018) Granular variable precision \(L\)-fuzzy rough sets based on residuated lattices. Fuzzy Sets Sys 336:148–166MathSciNetMATH Qiao JS, Hu BQ (2018) Granular variable precision \(L\)-fuzzy rough sets based on residuated lattices. Fuzzy Sets Sys 336:148–166MathSciNetMATH
Zurück zum Zitat Radzikowska AM, Kerre EE (2002) A comparative study of fuzzy rough sets. Fuzzy Sets Sys 126(2):137–155MathSciNetMATH Radzikowska AM, Kerre EE (2002) A comparative study of fuzzy rough sets. Fuzzy Sets Sys 126(2):137–155MathSciNetMATH
Zurück zum Zitat Singh S, Shreevastava S, Som T et al (2019) A fuzzy similarity-based rough set approach for attribute selection in set-valued information systems. Soft Comp 24(6):4675–4691MATH Singh S, Shreevastava S, Som T et al (2019) A fuzzy similarity-based rough set approach for attribute selection in set-valued information systems. Soft Comp 24(6):4675–4691MATH
Zurück zum Zitat Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundamenta Informaticae 27(2–3):245–253MathSciNetMATH Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundamenta Informaticae 27(2–3):245–253MathSciNetMATH
Zurück zum Zitat Syau YR, Lin EB (2014) Neighborhood systems and covering approximate spaces. Knowl-Based Sys 66:61–67 Syau YR, Lin EB (2014) Neighborhood systems and covering approximate spaces. Knowl-Based Sys 66:61–67
Zurück zum Zitat Tsang ECC, Chen DG, Yeung DS, Wang XZ, Lee JW (2008) Attributes reduction using fuzzy rough sets. IEEE Trans Fuzzy Sys 16(5):1130–1141 Tsang ECC, Chen DG, Yeung DS, Wang XZ, Lee JW (2008) Attributes reduction using fuzzy rough sets. IEEE Trans Fuzzy Sys 16(5):1130–1141
Zurück zum Zitat Wang CY, Hu BQ (2015) Granular variable precision fuzzy rough sets with general fuzzy relations. Fuzzy Sets Sys 275:39–57MathSciNetMATH Wang CY, Hu BQ (2015) Granular variable precision fuzzy rough sets with general fuzzy relations. Fuzzy Sets Sys 275:39–57MathSciNetMATH
Zurück zum Zitat Wang CY, Wan LJ (2021) New results on granular variable precision fuzzy rough sets based on fuzzy (co) implications. Fuzzy Sets Sys 423:149–169MathSciNet Wang CY, Wan LJ (2021) New results on granular variable precision fuzzy rough sets based on fuzzy (co) implications. Fuzzy Sets Sys 423:149–169MathSciNet
Zurück zum Zitat Wang CZ, Hu QH, Wang XZ, Chen DG, Qian YH, Dong Z (2017) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Sys 29(7):2986–2999MathSciNet Wang CZ, Hu QH, Wang XZ, Chen DG, Qian YH, Dong Z (2017) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Sys 29(7):2986–2999MathSciNet
Zurück zum Zitat Wu HS, Liu GL (2020) The relationships between topologies and generalized rough sets. Int J Appro Reason 119:313–324MathSciNetMATH Wu HS, Liu GL (2020) The relationships between topologies and generalized rough sets. Int J Appro Reason 119:313–324MathSciNetMATH
Zurück zum Zitat Wu WZ, Zhang WX (2004) Constructive and axiomatic approaches of fuzzy approximation operators. Inf Sci 159(3–4):233–254MathSciNetMATH Wu WZ, Zhang WX (2004) Constructive and axiomatic approaches of fuzzy approximation operators. Inf Sci 159(3–4):233–254MathSciNetMATH
Zurück zum Zitat Wu WZ, Leung Y, Mi JS (2005) On characterizations of \((I, T)\)-fuzzy rough approximation operators. Fuzzy Sets Sys 154(1):76–102MathSciNetMATH Wu WZ, Leung Y, Mi JS (2005) On characterizations of \((I, T)\)-fuzzy rough approximation operators. Fuzzy Sets Sys 154(1):76–102MathSciNetMATH
Zurück zum Zitat Wu WZ, Leung Y, Shao MW (2013) Generalized fuzzy rough approximation operators determined by fuzzy implicators. Int J Approx Reason 54(9):1388–1409 Wu WZ, Leung Y, Shao MW (2013) Generalized fuzzy rough approximation operators determined by fuzzy implicators. Int J Approx Reason 54(9):1388–1409
Zurück zum Zitat Xie G, Zhang J, Lai KK, Yu L (2008) Variable precision rough set for group decision-making: an application. Int J Approx Reason 49(2):331–343 Xie G, Zhang J, Lai KK, Yu L (2008) Variable precision rough set for group decision-making: an application. Int J Approx Reason 49(2):331–343
Zurück zum Zitat Yang B, Hu BQ (2017) On some types of fuzzy covering-based rough sets. Fuzzy Sets Sys 312:36–65MathSciNetMATH Yang B, Hu BQ (2017) On some types of fuzzy covering-based rough sets. Fuzzy Sets Sys 312:36–65MathSciNetMATH
Zurück zum Zitat Yang B, Hu BQ (2019) Fuzzy neighborhood operators and derived fuzzy coverings. Fuzzy Sets Sys 370:1–33MathSciNetMATH Yang B, Hu BQ (2019) Fuzzy neighborhood operators and derived fuzzy coverings. Fuzzy Sets Sys 370:1–33MathSciNetMATH
Zurück zum Zitat Yang T, Zhong XR, Lang GM, Qian YH, Dai JH (2020) Granular matrix: a new approach for granular structure reduction and redundancy evaluation. IEEE Trans Fuzzy Sys 28(12):3133–3144 Yang T, Zhong XR, Lang GM, Qian YH, Dai JH (2020) Granular matrix: a new approach for granular structure reduction and redundancy evaluation. IEEE Trans Fuzzy Sys 28(12):3133–3144
Zurück zum Zitat Yao YY (1996) Two views of the theory of rough sets in finite universes. Int J Approx Reason 15(4):291–317MathSciNetMATH Yao YY (1996) Two views of the theory of rough sets in finite universes. Int J Approx Reason 15(4):291–317MathSciNetMATH
Zurück zum Zitat Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109(1–4):21–47MathSciNetMATH Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109(1–4):21–47MathSciNetMATH
Zurück zum Zitat Yao YY (2021) Set-theoretic models of three-way decision. Granular Comp 6(1):133–148MathSciNet Yao YY (2021) Set-theoretic models of three-way decision. Granular Comp 6(1):133–148MathSciNet
Zurück zum Zitat Yao YQ, Mi JS, Li ZJ (2014) A novel variable precision \((\theta ,\sigma )\)-fuzzy rough set model based on fuzzy granules. Fuzzy Sets Sys 236:58–72MathSciNetMATH Yao YQ, Mi JS, Li ZJ (2014) A novel variable precision \((\theta ,\sigma )\)-fuzzy rough set model based on fuzzy granules. Fuzzy Sets Sys 236:58–72MathSciNetMATH
Zurück zum Zitat Ye J, Zhan JM, Sun BZ (2021) A three-way decision method based on fuzzy rough set models under incomplete environments. Inf Sci 577:22–48MathSciNet Ye J, Zhan JM, Sun BZ (2021) A three-way decision method based on fuzzy rough set models under incomplete environments. Inf Sci 577:22–48MathSciNet
Zurück zum Zitat Zhang K, Dai JH (2022) Redefined fuzzy rough set models in fuzzy \(\beta \)-covering group approximation spaces. Fuzzy Sets Sys 442:109–154MathSciNet Zhang K, Dai JH (2022) Redefined fuzzy rough set models in fuzzy \(\beta \)-covering group approximation spaces. Fuzzy Sets Sys 442:109–154MathSciNet
Zurück zum Zitat Zhang XH, Wang JQ (2020) Fuzzy \(\beta \)-covering approximation spaces. Int J Approx Reason 126:27–47MathSciNetMATH Zhang XH, Wang JQ (2020) Fuzzy \(\beta \)-covering approximation spaces. Int J Approx Reason 126:27–47MathSciNetMATH
Zurück zum Zitat Zhang K, Dai JH, Zhan JM (2021) A new classification and ranking decision method based on three-way decision theory and TOPSIS models. Inf Sci 568:54–85MathSciNet Zhang K, Dai JH, Zhan JM (2021) A new classification and ranking decision method based on three-way decision theory and TOPSIS models. Inf Sci 568:54–85MathSciNet
Zurück zum Zitat Zhang K, Zhan JM, Wu WZ (2021) On multicriteria decision-making method based on a fuzzy rough set model with fuzzy \(\alpha \)-neighborhoods. IEEE Trans Fuzzy Sys 29(9):2491–2505 Zhang K, Zhan JM, Wu WZ (2021) On multicriteria decision-making method based on a fuzzy rough set model with fuzzy \(\alpha \)-neighborhoods. IEEE Trans Fuzzy Sys 29(9):2491–2505
Zurück zum Zitat Zhao XR, Hu BQ (2015) Fuzzy variable precision rough sets based on residuated lattices. Int J General Sys 44(7–8):743–765MathSciNetMATH Zhao XR, Hu BQ (2015) Fuzzy variable precision rough sets based on residuated lattices. Int J General Sys 44(7–8):743–765MathSciNetMATH
Zurück zum Zitat Zhao FF, Li LQ (2018) Axiomatization on generalized neighborhood system-based rough sets. Soft Comp 22(18):6099–6110MATH Zhao FF, Li LQ (2018) Axiomatization on generalized neighborhood system-based rough sets. Soft Comp 22(18):6099–6110MATH
Zurück zum Zitat Zhao SY, Tsang ECC, Chen DG (2009) The model of fuzzy variable precision rough sets. IEEE Trans Fuzzy Sys 17(2):451–467 Zhao SY, Tsang ECC, Chen DG (2009) The model of fuzzy variable precision rough sets. IEEE Trans Fuzzy Sys 17(2):451–467
Zurück zum Zitat Zhou JL, Xu FS, Guan YY et al (2021) Three types of fuzzy covering-based rough set models. Fuzzy Sets Sys 423:122–148MathSciNet Zhou JL, Xu FS, Guan YY et al (2021) Three types of fuzzy covering-based rough set models. Fuzzy Sets Sys 423:122–148MathSciNet
Zurück zum Zitat Zhu W (2009) Relationship between generalized rough sets based on binary relation and covering. Inf Sci 179(3):210–225MathSciNetMATH Zhu W (2009) Relationship between generalized rough sets based on binary relation and covering. Inf Sci 179(3):210–225MathSciNetMATH
Metadaten
Titel
A novel granular variable precision fuzzy rough set model and its application in fuzzy decision system
verfasst von
Dan-Dan Zou
Yao-Liang Xu
Ling-Qiang Li
Wei-Zhi Wu
Publikationsdatum
07.01.2023
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 13/2023
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-022-07796-0

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