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Uncertainty representation in software models: a survey

Abstract

This paper provides a comprehensive overview and analysis of research work on how uncertainty is currently represented in software models. The survey presents the definitions and current research status of different proposals for addressing uncertainty modeling and introduces a classification framework that allows to compare and classify existing proposals, analyze their current status and identify new trends. In addition, we discuss possible future research directions, opportunities and challenges.

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Notes

  1. 1.

    http://www.jabref.org/.

  2. 2.

    https://www.zotero.org/.

  3. 3.

    Verification and validation are two controversial terms, to which different people assign different meanings. In this context we will use the meanings defined and used in ISO standards [162].

References

Primary Studies

  1. 1.

    Agli, H., Bonnard, P., Gonzales, C., Wuillemin, P.: Business rules uncertainty management with probabilistic relational models. In: Proceedings of RuleML’16, LNCS, vol. 9718, pp. 53–67. Springer (2016). https://doi.org/10.1007/978-3-319-42019-6_4

  2. 2.

    Ali, S., Basit-Ur-Rahim, M.A., Arif, F.: Formal verification of time constrains SysML internal block diagram using PRISM. In: Proceedings of ICCSA’15, pp. 62–66. IEEE Computer Society, USA (2015). https://doi.org/10.1109/ICCSA.2015.11

  3. 3.

    Bagheri, E., Ghorbani, A.A.: Experiences on the belief-theoretic integration of para-consistent conceptual models. In: Proceedings of ASWEC’08, pp. 357–366. IEEE (2008). https://doi.org/10.1109/ASWEC.2008.4483224

  4. 4.

    Bagheri, E., Ghorbani, A.A.: A belief-theoretic framework for the collaborative development and integration of para-consistent conceptual models. J. Syst. Softw. 82(4), 707–729 (2009). https://doi.org/10.1016/j.jss.2008.10.012

    Article  Google Scholar 

  5. 5.

    Baresi, L., Pasquale, L., Spoletini, P.: Fuzzy goals for requirements-driven adaptation. In: 2010 18th IEEE International Requirements Engineering Conference. IEEE (2010). https://doi.org/10.1109/re.2010.25

  6. 6.

    Bertoa, M.F., Burgueño, L., Moreno, N., Vallecillo, A.: Incorporating measurement uncertainty into OCL/UML primitive datatypes. Softw. Syst. Model. (2019). https://doi.org/10.1007/s10270-019-00741-0

    Article  Google Scholar 

  7. 7.

    Bertoa, M.F., Moreno, N., Barquero, G., Burgueño, L., Troya, J., Vallecillo, A.: Expressing measurement uncertainty in OCL/UML datatypes. In: Proceedings of ECMFA’18, LNCS, vol. 10890, pp. 46–62. Springer (2018). https://doi.org/10.1007/978-3-319-92997-2_4

  8. 8.

    Blanco, I.J., Marin, N., Pons, O., Vila, M.A.: Softening the object-oriented database model: imprecision, uncertainty, and fuzzy types. In: Proceedings of NAFIPS’01, vol. 4, pp. 2323–2328 (2001). https://doi.org/10.1109/NAFIPS.2001.944435

  9. 9.

    Brambilla, M., Eramo, R., Pierantonio, A., Rosa, G., Umuhoza, E.: Enhancing flexibility in user interaction modeling by adding design uncertainty to IFML. In: Proceedings of FLEXMDE@MODELS’17, CEUR Workshop Proceedings, vol. 2019, pp. 435–440. CEUR-WS.org (2017). URL http://ceur-ws.org/Vol-2019/flexmde_9.pdf

  10. 10.

    Bucaioni, A., Cicchetti, A., Ciccozzi, F., Mubeen, S., Pierantonio, A., Sjödin, M.: Handling uncertainty in automatically generated implementation models in the automotive domain. In: Proceedings of SEAA’16, pp. 173–180 (2016). https://doi.org/10.1109/SEAA.2016.32

  11. 11.

    Burgueño, L., Bertoa, M.F., Moreno, N., Vallecillo, A.: Expressing confidence in models and in model transformation elements. In: Proceedings of MODELS’18, pp. 57–66. ACM (2018). https://doi.org/10.1145/3239372.3239394

  12. 12.

    Burgueño, L., Clarisó, R., Cabot, J., Gérard, S., Vallecillo, A.: Belief uncertainty in software models. In: Proceedings of MiSE@ICSE’19, pp. 19–26. IEEE (2019). https://doi.org/10.1109/MiSE.2019.00011

  13. 13.

    Burgueño, L., Mayerhofer, T., Wimmer, M., Vallecillo, A.: Using physical quantities in robot software models. In: Proceedings of RoSE@MODELS’18, pp. 23–28. ACM (2018). https://doi.org/10.1145/3196558.3196562

  14. 14.

    Burgueño, L., Mayerhofer, T., Wimmer, M., Vallecillo, A.: Specifying quantities in software models. Inf. Softw. Technol. 113, 82–97 (2019). https://doi.org/10.1016/j.infsof.2019.05.006

    Article  Google Scholar 

  15. 15.

    Cámara, J., Peng, W., Garlan, D., Schmerl, B.R.: Reasoning about sensing uncertainty and its reduction in decision-making for self-adaptation. Sci. Comput. Program. 167, 51–69 (2018). https://doi.org/10.1016/j.scico.2018.07.002

    Article  MATH  Google Scholar 

  16. 16.

    Chang, E.J., Hussain, F.K., Dillon, T.S.: Fuzzy nature of trust and dynamic trust modeling in service oriented environments. In: Proceedings of SWS@CCS’05, pp. 75–83. ACM (2005). https://doi.org/10.1145/1103022.1103036

  17. 17.

    Chechik, M., Kokaly, S., Rahimi, M., Salay, R., Viger, T.: Uncertainty, modeling and safety assurance: towards a unified framework. In: Proceedings of VSTTE’19, LNCS, vol. 12031, pp. 19–29. Springer (2019). https://doi.org/10.1007/978-3-030-41600-3_2

  18. 18.

    Chen, X., Cheng, H., Wang, H., Li, W.: Fuzzy spatiotemporal object modeling based on UML class diagram. J. Intell. Fuzzy Syst. 33(5), 2727–2736 (2017). https://doi.org/10.3233/JIFS-169322

    Article  Google Scholar 

  19. 19.

    Chen, X., Yan, L., Li, W., Ma, Z.: Reengineering fuzzy spatiotemporal UML data model into fuzzy spatiotemporal XML model. IEEE Access 5, 17975–17987 (2017). https://doi.org/10.1109/ACCESS.2017.2745540

    Article  Google Scholar 

  20. 20.

    Cheng, B.H.C., Sawyer, P., Bencomo, N., Whittle, J.: A goal-based modeling approach to develop requirements of an adaptive system with environmental uncertainty. In: Proceedings of MODELS’09, LNCS, vol. 5795, pp. 468–483. Springer (2009). https://doi.org/10.1007/978-3-642-04425-0_36

  21. 21.

    Cheng, S.W., Garlan, D.: Handling uncertainty in autonomic systems. In: Proceedings of IWLU@ASE’07. ACM (2007). URL http://se.cs.toronto.edu/IWLU/papers/Autonomic_Cheng.pdf

  22. 22.

    Cheung, L., Golubchik, L., Medvidovic, N., Sukhatme, G.S.: Identifying and addressing uncertainty in architecture-level software reliability modeling. In: Proceedings of IPDPS’07, pp. 1–6. IEEE (2007). https://doi.org/10.1109/IPDPS.2007.370524

  23. 23.

    Crossland, R., Williams, J.H.S., McMahon, C.A.: An object-oriented modeling framework for representing uncertainty in early variant design. Res. Eng. Design 14(3), 173–183 (2003). https://doi.org/10.1007/s00163-003-0039-z

    Article  Google Scholar 

  24. 24.

    D’Emilia, G., Paolone, G., Natale, E., Gaspari, A., Villano, D.D.: Business modeling of a measurement-based context: a methodological process. In: Proceedings of ICSOFT-EA’15’, vol. 1, pp. 1–8. SciTePress (2015). https://doi.org/10.5220/0005499402690276

  25. 25.

    Diskin, Z., Eramo, R., Pierantonio, A., Czarnecki, K.: Incorporating uncertainty into bidirectional model transformations and their delta-lens formalization. In: Proceedings of BX@ETAPS’16, CEUR Workshop Proceedings, vol. 1571, pp. 15–31. CEUR-WS.org (2016). http://ceur-ws.org/Vol-1571/paper_9.pdf

  26. 26.

    Dong, Q., Wang, Z., Zhu, W., He, H.: Capability requirements modeling and verification based on fuzzy ontology. J. Syst. Eng. Electron. 23(1), 78–87 (2012). https://doi.org/10.1109/JSEE.2012.00011

    Article  Google Scholar 

  27. 27.

    Eramo, R., Pierantonio, A., Rosa, G.: Managing uncertainty in bidirectional model transformations. In: Proceedings of SLE’15, pp. 49–58. ACM (2015). https://doi.org/10.1145/2814251.2814259

  28. 28.

    Eramo, R., Pierantonio, A., Rosa, G.: Approaching collaborative modeling as an uncertainty reduction process. In: Proceedings of COMMitMDE@MODELS’16, CEUR Workshop Proceedings, vol. 1717, pp. 27–34. CEUR-WS.org (2016). http://ceur-ws.org/Vol-1717/paper7.pdf

  29. 29.

    Esfahani, N., Elkhodary, A.M., Malek, S.: A learning-based framework for engineering feature-oriented self-adaptive software systems. IEEE Trans. Softw. Eng. 39(11), 1467–1493 (2013). https://doi.org/10.1109/TSE.2013.37

    Article  Google Scholar 

  30. 30.

    Esfahani, N., Malek, S., Razavi, K.: Guidearch: guiding the exploration of architectural solution space under uncertainty. In: Proceedings of ICSE’13, pp. 43–52. IEEE Computer Society (2013). https://doi.org/10.1109/ICSE.2013.6606550

  31. 31.

    Famelis, M., Chechik, M.: Managing design-time uncertainty. Softw. Syst. Model. 18(2), 1249–1284 (2019). https://doi.org/10.1007/s10270-017-0594-9

    Article  Google Scholar 

  32. 32.

    Famelis, M., Rubin, J., Czarnecki, K., Salay, R., Chechik, M.: Software product lines with design choices: reasoning about variability and design uncertainty. In: Proceedings of MODELS’17. IEEE Computer Society (2017). https://doi.org/10.1109/models.2017.3

  33. 33.

    Famelis, M., Salay, R., Chechik, M.: Partial models: towards modeling and reasoning with uncertainty. In: Proceedings of ICSE’12, pp. 573–583. IEEE Press (2012). https://doi.org/10.1109/ICSE.2012.6227159

  34. 34.

    Famelis, M., Santosa, S.: MAV-Vis: a notation for model uncertainty. In: Proceedings of MiSE@ICSE’13, pp. 7–12. IEEE (2013). https://doi.org/10.1109/MiSE.2013.6595289

  35. 35.

    García-Valls, M., Perez-Palacin, D., Mirandola, R.: Pragmatic cyber physical systems design based on parametric models. J. Syst. Softw. 144, 559–572 (2018). https://doi.org/10.1016/j.jss.2018.06.044

    Article  Google Scholar 

  36. 36.

    Garousi, V.: Traffic-aware stress testing of distributed real-time systems based on UML models in the presence of time uncertainty. In: Proceedings of ICST’08, pp. 92–101. IEEE Computer Society (2008). https://doi.org/10.1109/ICST.2008.7

  37. 37.

    Garredu, S., Bisgambiglia, P.A., Vittori, E., Santucci, J.F.: A New Approach to Describe DEVS Models Using Both UML State Machine Diagrams and Fuzzy Logic. In: Proceedings of EMSS’10, pp. 215–221. SCS (2010)

  38. 38.

    Geng, S., Peng, J., Li, P.: Modeling and verification of cyber-physical systems under uncertainty. In: Proceedings of ICNC-FSKD’17, pp. 1491–1496 (2017). https://doi.org/10.1109/FSKD.2017.8392986

  39. 39.

    Giese, H., Bencomo, N., Pasquale, L., Ramirez, A.J., Inverardi, P., Wätzoldt, S., Clarke, S.: Living with uncertainty in the age of runtime models. In: Models@run.time, LNCS, vol. 8378, pp. 47–100. Springer (2014). https://doi.org/10.1007/978-3-319-08915-7_3

  40. 40.

    Gogolla, M., Vallecillo, A.: On softening OCL invariants. J. Object Technol. 18(2), 6:1–22 (2019). https://doi.org/10.5381/jot.2019.18.2.a6

    Article  Google Scholar 

  41. 41.

    Gonzalez-Perez, C.: Modelling temporality and subjectivity in ConML: short paper. In: Proceedings of RCIS’13, pp. 1–6. IEEE (2013). https://doi.org/10.1109/RCIS.2013.6577685

  42. 42.

    Hacks, S., Lichter, H.: A probabilistic enterprise architecture model evolution. In: Proceedings of EDOC’18’, pp. 51–57. IEEE Computer Society (2018). https://doi.org/10.1109/EDOC.2018.00017

  43. 43.

    Hall, B.D.: Component interfaces that support measurement uncertainty. Comput. Stand. Interfaces 28(3), 306–310 (2006). https://doi.org/10.1016/j.csi.2005.07.009

    Article  Google Scholar 

  44. 44.

    Han, D., Yang, Q., Xing, J.: Extending UML for the modeling of fuzzy self-adaptive software systems. In: Proceedings of CCDC’14, pp. 2400–2406. IEEE (2014). https://doi.org/10.1109/CCDC.2014.6852575

  45. 45.

    Han, D., Yang, Q., Xing, J., Li, J., Wang, H.: FAME: a UML-based framework for modeling fuzzy self-adaptive software. Inf. Softw. Technol. 76(C), 118–134 (2016). https://doi.org/10.1016/j.infsof.2016.04.014

    Article  Google Scholar 

  46. 46.

    Haroonabadi, A., Teshnehlab, M., Movaghar, A.: A novel method for modeling and evaluation of uncertain information systems. In: Proceedings of ICIT’08, pp. 238–243. IEEE Computer Society (2008). https://doi.org/10.1109/ICIT.2008.24

  47. 47.

    Jiménez-Ramírez, A., Weber, B., Barba, I., del Valle, C.: Generating optimized configurable business process models in scenarios subject to uncertainty. Inf. Softw. Technol. 57, 571–594 (2015). https://doi.org/10.1016/j.infsof.2014.06.006

    Article  Google Scholar 

  48. 48.

    Johnson, P., Iacob, M.E., Välja, M., Sinderen, M., Magnusson, C., Ladhe, T.: A method for predicting the probability of business network profitability. Inf. Syst. E-Bus. Manag. 12(4), 567–593 (2014). https://doi.org/10.1007/s10257-014-0237-4

    Article  Google Scholar 

  49. 49.

    Johnson, P., Ullberg, J., Buschle, M., Franke, U., Shahzad, K.: An architecture modeling framework for probabilistic prediction. Inf. Syst. E-Bus. Manag. 12(4), 595–622 (2014). https://doi.org/10.1007/s10257-014-0241-8

    Article  Google Scholar 

  50. 50.

    Khalfi, B., de Runz, C., Faiz, S., Akdag, H.: Modélisation conceptuelle d’objets géographiques imprécis et multiples : Une approche basée F-Perceptory. In: Proceedings of SAGEO’15, CEUR Workshop Proceedings, vol. 1535, pp. 297–311. CEUR-WS.org (2015). http://ceur-ws.org/Vol-1535/paper-21.pdf

  51. 51.

    Koehler, H., Link, S., Prade, H., Zhou, X.: Cardinality constraints for uncertain data. In: Proceedings of ER’14, LNCS, vol. 8824, pp. 108–121. Springer (2014). https://doi.org/10.1007/978-3-319-12206-9_9

  52. 52.

    Laghouaouta, Y., Laforcade, P.: Dealing with uncertainty in model transformations. In: Proceedings of SAC’20, pp. 1595—1603. ACM (2020). https://doi.org/10.1145/3341105.3373971

  53. 53.

    López-Landa, R., Noguez, J.: PRoModel: a model-driven software environment that facilitates and expedites the development of systems that handle uncertainty. In: Proceedings of SpringSim’12, p. 41. SCS/ACM (2012)

  54. 54.

    Ma, T., Ali, S., Yue, T., Elaasar, M.: Testing self-healing cyber-physical systems under uncertainty: a fragility-oriented approach. Softw. Qual. J. 27(2), 615–649 (2019). https://doi.org/10.1007/s11219-018-9437-3

    Article  Google Scholar 

  55. 55.

    Ma, Z.: The fuzzy ER/EER and UML data models, pp. 59–77 (2006). https://doi.org/10.1007/11353270_4

  56. 56.

    Ma, Z., Zhang, F., Yan, L., Cheng, J.: Fuzzy description logic and ontology extraction from fuzzy data models. In: Fuzzy knowledge management for the semantic web, vol. 306, pp. 99–156. Springer (2014). https://doi.org/10.1007/978-3-642-39283-2_5

  57. 57.

    Ma, Z.M.: Modeling Fuzzy Information in the EER and Nested Relational Database Models, pp. 123–146. Springer (2006). https://doi.org/10.1007/3-540-33289-8_5

  58. 58.

    Ma, Z.M., Yan, L.: Fuzzy XML data modeling with the UML and relational data models. Data Knowl. Eng. 63(3), 972–996 (2007). https://doi.org/10.1016/j.datak.2007.06.003

    Article  Google Scholar 

  59. 59.

    Ma, Z.M., Yan, L., Zhang, F.: Modeling fuzzy information in UML class diagrams and object-oriented database models. Fuzzy Sets Syst. 186(1), 26–46 (2012). https://doi.org/10.1016/j.fss.2011.06.015

    MathSciNet  Article  Google Scholar 

  60. 60.

    Ma, Z.M., Zhang, F., Yan, L.: Fuzzy information modeling in UML class diagram and relational database models. Appl. Soft Comput. 11(6), 4236–4245 (2011). https://doi.org/10.1016/j.asoc.2011.03.020

    Article  Google Scholar 

  61. 61.

    Ma, Z.M., Zhang, F., Yan, L., Cheng, J.: Representing and reasoning on fuzzy UML models: a description logic approach. Expert Syst. Appl. 38(3), 2536–2549 (2011). https://doi.org/10.1016/j.eswa.2010.08.042

    Article  Google Scholar 

  62. 62.

    Martín-Rodilla, P., Gonzalez-Perez, C.: Representing imprecise and uncertain knowledge in digital humanities: a theoretical framework and conml implementation with a real case study. In: Proceedings of TEEM’18, pp. 863–871. ACM (2018). https://doi.org/10.1145/3284179.3284318

  63. 63.

    Martin-Rodilla, P., Gonzalez-Perez, C.: Conceptualization and non-relational implementation of ontological and epistemic vagueness of information in digital humanities. Inform. (2019). https://doi.org/10.3390/informatics6020020

    Article  Google Scholar 

  64. 64.

    Martín-Rodilla, P., Gonzalez-Perez, M.P.F.C.: Qualifying and quantifying uncertainty in digital humanities: a fuzzy-logic approach. In: Proceedings of TEEM’19, pp. 788–794. ACM (2019). https://doi.org/10.1145/3362789.3362833

  65. 65.

    Mayerhofer, T., Wimmer, M., Vallecillo, A.: Adding uncertainty and units to quantity types in software models. In: Proceedings of SLE’16, pp. 118–131. ACM (2016). https://doi.org/10.1145/2997364.2997376

  66. 66.

    McKeever, S., Ye, J., Coyle, L., Dobson, S.: A context quality model to support transparent reasoning with uncertain context. In: Proceedings of QuaCon’09, LNCS, vol. 5786, pp. 65–75. Springer (2009). https://doi.org/10.1007/978-3-642-04559-2_6

  67. 67.

    Menghi, C., Spoletini, P., Chechik, M., Ghezzi, C.: A verification-driven framework for iterative design of controllers. Form. Asp. Comput. 31(5), 459–502 (2019). https://doi.org/10.1007/s00165-019-00484-1

    MathSciNet  Article  MATH  Google Scholar 

  68. 68.

    Motameni, H., Ghassempouri, T., Nematzadeh, H.: Evaluating the reliability of communication diagram using Fuzzy Petri net. In: Proceedings of ICSEES’11, pp. 520–523. IEEE (2011). https://doi.org/10.1109/ICSESS.2011.5982367

  69. 69.

    Nasiri, R., Moeini, A., Abdollahzadeh, A.: A new approach towards procurement of software models via distributed business models. J. Supercomput. 29(3), 287–302 (2004). https://doi.org/10.1023/B:SUPE.0000032782.92290.52

    Article  MATH  Google Scholar 

  70. 70.

    Object Management Group: Structured Metrics Metamodel (SMM) Specification. Version 1.2 (2018). OMG Document formal/18-05-01

  71. 71.

    Object Management Group: OMG Systems Modeling Language (SysML), version 1.6 (2019). OMG Document formal/19-11-01

  72. 72.

    Object Management Group: UML Profile for MARTE: Modeling and Analysis of Real-Time Embedded Systems. Version 1.2 (2019). OMG Document formal/19-04-01

  73. 73.

    Oquendo, F.: Coping with uncertainty in systems-of-systems architecture modeling on the IoT with SosADL. In: Proceedings of SoSE’19, pp. 131–136 (2019). https://doi.org/10.1109/SYSOSE.2019.8753842

  74. 74.

    Ortiz, V., Burgueño, L., Vallecillo, A., Gogolla, M.: Native support for UML and OCL primitive datatypes enriched with uncertainty in USE. In: Proceedings of OCL@MODELS’19, CEUR Workshop Proceedings, vol. 2513, pp. 59–66. CEUR-WS.org (2019). http://ceur-ws.org/Vol-2513/paper5.pdf

  75. 75.

    Ozgur, N.B., Koyuncu, M., Yazici, A.: An intelligent fuzzy object-oriented database framework for video database applications. Fuzzy Sets Syst. 160(15), 2253–2274 (2009). https://doi.org/10.1016/j.fss.2009.02.017

    MathSciNet  Article  Google Scholar 

  76. 76.

    Packevicius, S., Usaniov, A., Bareisa, E.: Software testing using imprecise OCL constraints as oracles. In: Proceedings of CompSysTech’07, pp. 1–6. ACM (2007). https://doi.org/10.1145/1330598.1330726

  77. 77.

    Refsdal, A., Runde, R.K., Stølen, K.: Underspecification, inherent nondeterminism and probability in sequence diagrams. In: Proceedings of FMOODS’06, LNCS, vol. 4037, pp. 138–155. Springer (2006). https://doi.org/10.1007/11768869_12

  78. 78.

    Refsdal, A., Runde, R.K., Stølen, K.: Stepwise refinement of sequence diagrams with soft real-time constraints. J. Comput. Syst. Sci. 81(7), 1221–1251 (2015). https://doi.org/10.1016/j.jcss.2015.03.003

    MathSciNet  Article  MATH  Google Scholar 

  79. 79.

    Refsdal, A., Solhaug, B., Stolen, K.: A UML-based method for the development of policies to support trust management. In: Trust Management II, vol. 263, pp. 33+. IFIP (2008). https://doi.org/10.1007/978-0-387-09428-1_3

  80. 80.

    Refsdal, A., Stølen, K.: Extending UML sequence diagrams to model trust-dependent behavior with the aim to support risk analysis. Sci. Comput. Program. 74(1–2), 34–42 (2008). https://doi.org/10.1016/j.scico.2008.09.003

    MathSciNet  Article  MATH  Google Scholar 

  81. 81.

    Robak, S., Pieczynski, A.: Employing fuzzy logic in feature diagrams to model variability in software product-lines. In: Proceedings of ECBS’03, pp. 305–311. IEEE Computer Society (2003). https://doi.org/10.1109/ECBS.2003.1194812

  82. 82.

    Runde, R.K., Refsdal, A., Stølen, K.: Relating computer systems to sequence diagrams: the impact of underspecification and inherent nondeterminism. Form. Asp. Comput. 25(2), 159–187 (2013). https://doi.org/10.1007/s00165-011-0192-5

    MathSciNet  Article  MATH  Google Scholar 

  83. 83.

    Salay, R., Chechik, M.: A generalized formal framework for partial modeling. In: Proceedings of FASE’15, LNCS, vol. 9033, pp. 133–148. Springer (2015). https://doi.org/10.1007/978-3-662-46675-9_9

  84. 84.

    Salay, R., Chechik, M., Famelis, M., Gorzny, J.: A methodology for verifying refinements of partial models. J. Object Technol. 14(3), 3:1–31 (2015). https://doi.org/10.5381/jot.2015.14.3.a3

    Article  Google Scholar 

  85. 85.

    Salay, R., Chechik, M., Horkoff, J., Sandro, A.D.: Managing requirements uncertainty with partial models. Requir. Eng. 18(2), 107–128 (2013). https://doi.org/10.1007/s00766-013-0170-y

    Article  Google Scholar 

  86. 86.

    Salay, R., Gorzny, J., Chechik, M.: Change propagation due to uncertainty change. In: Proceedings of FASE’13, LNCS, vol. 7793, pp. 21–36. Springer (2013). https://doi.org/10.1007/978-3-642-37057-1_3

  87. 87.

    Sedaghatbaf, A., Azgomi, M.A.: Reliability evaluation of UML/DAM software architectures under parameter uncertainty. IET Softw. 12(3), 236–244 (2018). https://doi.org/10.1049/iet-sen.2017.0077

    Article  Google Scholar 

  88. 88.

    Sheng, J., Yan, L., Ma, Z.: Modeling probabilistic data with fuzzy probability measures in UML class diagrams. In: Proceedings of IFSA/NAFIPS’19, Advances in Intelligent Systems and Computing, vol. 1000, pp. 589–600. Springer (2019). https://doi.org/10.1007/978-3-030-21920-8_52

  89. 89.

    Shin, S.Y., Chaouch, K., Nejati, S., Sabetzadeh, M., Briand, L.C., Zimmer, F.: HITECS: a UML profile and analysis framework for hardware-in-the-loop testing of cyber physical systems. In: Proceedings of MODELS’18, pp. 357–367. ACM (2018). https://doi.org/10.1145/3239372.3239382

  90. 90.

    Sibay, G.E., Braberman, V.A., Uchitel, S., Kramer, J.: Synthesizing modal transition systems from triggered scenarios. IEEE Trans. Softw. Eng. 39(7), 975–1001 (2013). https://doi.org/10.1109/TSE.2012.62

    Article  Google Scholar 

  91. 91.

    Sicilia, M.A., Diaz, P., Aedo, I., Garcia, E.: Fuzziness in adaptive hypermedia models. In: Proceedings of NAFIPS’02, pp. 268–273 (2002). https://doi.org/10.1109/NAFIPS.2002.1018068

  92. 92.

    Sicilia, M.A., Mastorakis, N.: Extending UML 1.5 for fuzzy conceptual modeling: an strictly additive approach. WSEAS Trans. Syst. 3(5), 2234–2239 (2004)

    Google Scholar 

  93. 93.

    de Soto, A.R., Capdevila, C.A., Fernández, E.C.: Fuzzy systems and neural networks XML schemas for soft computing. Mathw. Soft Comput. 10(2–3), 43–56 (2003)

    MATH  Google Scholar 

  94. 94.

    Stephenson, Z.R., Attwood, K., McDermid, J.A.: Product-line models to address requirements uncertainty, volatility and risk, pp. 111–131. Springer (2011). https://doi.org/10.1007/978-3-642-21001-3_8

  95. 95.

    Thomas, O., Dollmann, T.: Fuzzy-EPC markup language: XML based interchange formats for fuzzy process models. In: Soft Computing in XML Data Management, vol. 255, pp. 227–257. Springer (2010). https://doi.org/10.1007/978-3-642-14010-5_9

  96. 96.

    Troegner, D.: Combination of fuzzy sets with the object constraint language (OCL). In: Proceedings of Informatik’10, LNI, vol. P-176, pp. 705–710 (2010). https://dl.gi.de/20.500.12116/19308

  97. 97.

    Tseng, C., Khamisy, W., Vu, T.: Universal fuzzy system representation with XML. Comput. Stand. Interfaces 28(2), 218–230 (2005). https://doi.org/10.1016/j.csi.2004.11.005

    Article  Google Scholar 

  98. 98.

    Tudoroiu, R., Astilean, A., Letia, T., Neacsu, G., Maroszy, Z., Tudoroiu, N.: Fuzzy UML and petri nets modeling investigations on the pollution impact on the air quality in the vicinity of the black sea constanta romanian resort. In: Proceedings of FedCSIS’11, pp. 763–766 (2011)

  99. 99.

    Turowski, K., Weng, U.: Representing and processing fuzzy information—an xml-based approach. Knowl. Based Syst. 15(1–2), 67–75 (2002). https://doi.org/10.1016/S0950-7051(01)00122-8

    Article  Google Scholar 

  100. 100.

    Ubayashi, N., Kamei, Y., Sato, R.: Modular programming and reasoning for living with uncertainty. In: Proceedings of ICSOFT’18, vol. 1077, pp. 220–244. Springer (2019). https://doi.org/10.1007/978-3-030-29157-0_10

  101. 101.

    Uchitel, S., Brunet, G., Chechik, M.: Synthesis of partial behavior models from properties and scenarios. IEEE Trans. Softw. Eng. 35(3), 384–406 (2009). https://doi.org/10.1109/TSE.2008.107

    Article  Google Scholar 

  102. 102.

    Vallecillo, A., Morcillo, C., Orue, P.: Expressing measurement uncertainty in software models. In: Proceedings of QUATIC’16, pp. 15–24 (2016). https://doi.org/10.1109/QUATIC.2016.013

  103. 103.

    Voudouris, V.: Towards a unifying formalisation of geographic representation: the object-field model with uncertainty and semantics. Int. J. Geograph. Inf. Sci. 24(12), 1811–1828 (2010). https://doi.org/10.1080/13658816.2010.488237

    Article  Google Scholar 

  104. 104.

    Voudouris, V., Wood, J., Fisher, P.F.: Collaborative geovisualization: object-field representations with semantic and uncertainty information. In: Proceedings of OTM’05 Workshops, LNCS, vol. 3762, pp. 1056–1065. Springer (2005). https://doi.org/10.1007/11575863_128

  105. 105.

    Voudouris, V., Wood, J., Fisher, P.F.: Capturing and Representing Conceptualization Uncertainty Interactively Using Object-Fields, pp. 755–770. Springer, Berlin (2006). https://doi.org/10.1007/3-540-35589-8_47

  106. 106.

    Wang, Y., Bai, L.: Fuzzy spatiotemporal data modeling based on UML. IEEE Access 7, 45405–45416 (2019). https://doi.org/10.1109/ACCESS.2019.2908224

    Article  Google Scholar 

  107. 107.

    Whittle, J., Sawyer, P., Bencomo, N., Cheng, B.H.C., Bruel, J.: RELAX: incorporating uncertainty into the specification of self-adaptive systems. In: Proceedings of RE’09, pp. 79–88. IEEE Computer Society (2009). https://doi.org/10.1109/RE.2009.36

  108. 108.

    Whittle, J., Sawyer, P., Bencomo, N., Cheng, B.H.C., Bruel, J.: RELAX: a language to address uncertainty in self-adaptive systems requirements. Requir. Eng. 15(2), 177–196 (2010). https://doi.org/10.1007/s00766-010-0101-0

    Article  Google Scholar 

  109. 109.

    Xiao, J., Pinel, P., Pi, L., Aranega, V., Baron, C.: Modeling uncertain and imprecise information in process modeling with UML. In: Proceedings of ICMD’08, pp. 237–240. Computer Society of India/Allied Publishers (2008)

  110. 110.

    Xu, S., Miao, W., Kunz, T., Wei, T., Chen, M.: Quantitative analysis of variation-aware internet of things designs using statistical model checking. In: Proceedings of QRS’16, pp. 274–285. IEEE (2016). https://doi.org/10.1109/QRS.2016.39

  111. 111.

    Yan, L., Ma, Z.: A probabilistic object-oriented database model with fuzzy measures, pp. 23–38. Springer, Berlin (2013). https://doi.org/10.1007/978-3-642-37509-5_2

  112. 112.

    Yan, L., Ma, Z.: A probabilistic object-oriented database model with fuzzy probability measures and its algebraic operations. J. Intell. Fuzzy Syst. 28(5), 1969–1984 (2015). https://doi.org/10.3233/IFS-141307

    MathSciNet  Article  MATH  Google Scholar 

  113. 113.

    Yan, L., Ma, Z.: A formal approach for graphically building fuzzy XML model. Int. J. Intell. Syst. 34(11), 3058–3076 (2019). https://doi.org/10.1002/int.22188

    Article  Google Scholar 

  114. 114.

    Yan, L., Ma, Z.M.: Extending engineering data model for web-based fuzzy information modeling. Integr. Comput. Aided Eng. 20(4), 407–420 (2013). https://doi.org/10.3233/ICA-130440

    Article  Google Scholar 

  115. 115.

    Yang, Z., Jin, Z., Li, Z.: Modeling Uncertainty and Evolving Self-Adaptive Software: A Fuzzy Theory Based Requirements Engineering Approach. CoRR arXiv:abs/1704.00873 (2017)

  116. 116.

    Yazici, A., Zhu, Q., Sun, N.: Semantic data modeling of spatiotemporal database applications. Int. J. Intell. Syst. 16(7), 881–904 (2001). https://doi.org/10.1002/int.1040

    Article  MATH  Google Scholar 

  117. 117.

    Zhang, F., Cheng, J.: Verification of fuzzy UML models with fuzzy description logic. Appl. Soft Comput. 73, 134–152 (2018). https://doi.org/10.1016/j.asoc.2018.08.025

    Article  Google Scholar 

  118. 118.

    Zhang, F., Ma, Z.M.: Construction of fuzzy ontologies from fuzzy UML models. Int. J. Comput. Intell. Syst. 6(3), 442–472 (2013). https://doi.org/10.1080/18756891.2013.780735

    Article  Google Scholar 

  119. 119.

    Zhang, M., Ali, S., Yue, T., Norgre, R.: Uncertainty-wise evolution of test ready models. Inf. Softw. Technol. 87, 140–159 (2017). https://doi.org/10.1016/j.infsof.2017.03.003

    Article  Google Scholar 

  120. 120.

    Zhang, M., Ali, S., Yue, T., Norgren, R., Okariz, O.: Uncertainty-wise cyber-physical system test modeling. Softw. Syst. Model. 18(2), 1379–1418 (2019). https://doi.org/10.1007/s10270-017-0609-6

    Article  Google Scholar 

  121. 121.

    Zhang, M., Selic, B., Ali, S., Yue, T., Okariz, O., Norgren, R.: Understanding uncertainty in cyber-physical systems: a conceptual model. In: Proceedings of ECMFA’16, LNCS, vol. 9764, pp. 247–264. Springer (2016). https://doi.org/10.1007/978-3-319-42061-5_16

  122. 122.

    Zhang, M., Yue, T., Ali, S., Selic, B., Okariz, O., Norgren, R., Intxausti, K.: Specifying uncertainty in use case models. J. Syst. Softw. 144, 573–603 (2018). https://doi.org/10.1016/j.jss.2018.06.075

    Article  Google Scholar 

  123. 123.

    Zhou, B., Lu, J., Wang, Z., Zhang, Y., Miao, Z.: Formalizing fuzzy UML class diagrams with fuzzy description logics. In: Proceedings of IITA’09, vol. 1, pp. 171–174 (2009). https://doi.org/10.1109/IITA.2009.97

References

  1. 124.

    Albers, A., Zingel, C.: Extending SysML for engineering designers by integration of the contact and channel—approach (C&C\({}^{\text{2 }}\)-A) for function-based modeling of technical systems. Procedia Comput. Sci. 16, 353–362 (2013). https://doi.org/10.1016/j.procs.2013.01.037

    Article  Google Scholar 

  2. 125.

    Alevizos, E., Skarlatidis, A., Artikis, A., Paliouras, G.: Probabilistic complex event recognition: a survey. ACM Comput. Surv. 50(5), 71:1–71:31 (2017). https://doi.org/10.1145/3117809

    Article  Google Scholar 

  3. 126.

    Association for Computing Machinery: ACM Computing Classification System (2012). https://dl.acm.org/ccs

  4. 127.

    Balsamo, S., Marco, A.D., Inverardi, P., Simeoni, M.: Model-based performance prediction in software development: a survey. IEEE Trans. Softw. Eng. 30(5), 295–310 (2004). https://doi.org/10.1109/TSE.2004.9

    Article  Google Scholar 

  5. 128.

    Bernardi, S., Merseguer, J., Petriu, D.C.: Dependability modeling and analysis of software systems specified with UML. ACM Comput. Surv. 45(1), 2:1–2:48 (2012). https://doi.org/10.1145/2379776.2379778

    Article  MATH  Google Scholar 

  6. 129.

    Bernardi, S., Merseguer, J., Petriu, D.C.: Model-Driven Dependability Assessment of Software Systems. Springer, Heidelberg (2013)

    Book  Google Scholar 

  7. 130.

    Blair, G.S., Bencomo, N., France, R.B.: Models@run.time. IEEE Comput. 42(10), 22–27 (2009). https://doi.org/10.1109/MC.2009.326

    Article  Google Scholar 

  8. 131.

    Bosc, P., Pivert, O.: Modeling and querying uncertain relational databases: a survey of approaches based on the possible worlds semantics. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 18(5), 565–603 (2010). https://doi.org/10.1142/S0218488510006702

    MathSciNet  Article  Google Scholar 

  9. 132.

    Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Proceedings of CAV’99, LNCS, vol. 1633, pp. 274–287. Springer (1999). https://doi.org/10.1007/3-540-48683-6_25

  10. 133.

    Bucchiarone, A., Cabot, J., Paige, R.F., Pierantonio, A.: Grand challenges in model-driven engineering: an analysis of the state of the research. Softw. Syst. Model. 19(1), 5–13 (2020). https://doi.org/10.1007/s10270-019-00773-6

    Article  Google Scholar 

  11. 134.

    Büttner, F., Gogolla, M.: On OCL-based imperative languages. Sci. Comput. Program. 92, 162–178 (2014). https://doi.org/10.1016/j.scico.2013.10.003

    Article  Google Scholar 

  12. 135.

    Cámara, J., Garlan, D., Kang, W.G., Peng, W., Schmerl, B.R.: Uncertainty in self-adaptive systems: categories, management, and perspectives. Technical Report CMU-ISR-17-110, Carnegie Mellon University (2017). http://reports-archive.adm.cs.cmu.edu/anon/isr2017/CMU-ISR-17-110.pdf

  13. 136.

    Chen, M.: A BDI agents programming language based fuzzy beliefs. In: Proceedings of IHMSC’15, vol. 1, pp. 334–337 (2015). https://doi.org/10.1109/IHMSC.2015.170

  14. 137.

    Ciccozzi, F., Malavolta, I., Selic, B.: Execution of UML models: a systematic review of research and practice. Softw. Syst. Model. 18(3), 2313–2360 (2019). https://doi.org/10.1007/s10270-018-0675-4

    Article  Google Scholar 

  15. 138.

    Console, M., Guagliardo, P., Libkin, L.: Propositional and predicate logics of incomplete information. In: Proceedings of KR’18, pp. 592–601. AAAI Press (2018)

  16. 139.

    Cortellessa, V., Marco, A.D., Inverardi, P.: Model-Based Software Performance Analysis. Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-13621-4

    Book  Google Scholar 

  17. 140.

    Cova, T.J., Goodchild, M.F.: Extending geographical representation to include fields of spatial objects. Int. J. Geograph. Inf. Sci. 16(6), 509–532 (2002). https://doi.org/10.1080/13658810210137040

    Article  Google Scholar 

  18. 141.

    Dajsuren, Y., van den Brand, M. (eds.): Automotive Systems and Software Engineering—State of the Art and Future Trends. Springer, Berlin (2019). https://doi.org/10.1007/978-3-030-12157-0

  19. 142.

    Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  20. 143.

    Dugan, J.B., Bavuso, S.J., Boyd, M.A.: Dynamic fault-tree models for fault-tolerant computer systems. IEEE Trans. Reliab. 41(3), 363–377 (1992). https://doi.org/10.1109/24.159800

    Article  MATH  Google Scholar 

  21. 144.

    Esfahani, N., Malek, S.: Uncertainty in self-adaptive software systems. In: R. de Lemos, et al. (eds.) Software Engineering for Self-Adaptive Systems II, LNCS, vol. 7475, pp. 214–238. Springer (2013)

  22. 145.

    Feller, W.: An Introduction to Probability Theory and Its Applications. Wiley, Hoboken (2008)

    MATH  Google Scholar 

  23. 146.

    de Finetti, B.: Theory of Probability: A Critical Introductory Treatment. Wiley, Hoboken (2017). https://doi.org/10.1002/9781119286387

    Book  MATH  Google Scholar 

  24. 147.

    Garlan, D.: Software engineering in an uncertain world. In: Proceedings of the FoSER Workshop at FSE/SDP 2010, pp. 125–128. ACM (2010). https://doi.org/10.1145/1882362.1882389

  25. 148.

    Gnesi, S., Latella, D., Massink, M.: A stochastic extension of a behavioural subset of UML statechart diagrams. In: Proceedings of HASE’00, pp. 55–64. IEEE Computer Society (2000). https://doi.org/10.1109/HASE.2000.895442

  26. 149.

    Gogolla, M., Büttner, F., Richters, M.: USE: a UML-based specification environment for validating UML and OCL. Sci. Comput. Program. 69(1–3), 27–34 (2007). https://doi.org/10.1016/j.scico.2007.01.013

    MathSciNet  Article  MATH  Google Scholar 

  27. 150.

    González, C.A., Cabot, J.: Formal verification of static software models in MDE: a systematic review. Inf. Softw. Technol. 56(8), 821–838 (2014). https://doi.org/10.1016/j.infsof.2014.03.003

    Article  Google Scholar 

  28. 151.

    Greengard, S.: The Internet of Things. MIT Press, Cambridge, MA (2015)

    Book  Google Scholar 

  29. 152.

    Hall, B.D.: GTC: The GUM Tree Calculator (2020). https://github.com/MSLNZ/GTC

  30. 153.

    Hall, B.D., White, D.R.: An Introduction to Measurement Uncertainty. Measurement Standards Laboratory of New Zealand (2018). https://doi.org/10.5281/zenodo.3872590

  31. 154.

    Hanss, M.: Applied Fuzzy Arithmetic. An Introduction with Engineering Applications. Springer, Berlin (2005)

    MATH  Google Scholar 

  32. 155.

    Harel, D., Marelly, R.: Come, Let’s Play, Scenario-Based Programming Using LSCs and the Play-Engine. Springer, Berlin (2003). https://doi.org/10.1007/978-3-642-19029-2

  33. 156.

    Hariri, R.H., Fredericks, E.M., Bowers, K.M.: Uncertainty in big data analytics: survey, opportunities, and challenges. J. Big Data 6, 44 (2019). https://doi.org/10.1186/s40537-019-0206-3

    Article  Google Scholar 

  34. 157.

    Hermanns, H., Herzog, U., Katoen, J.: Process algebra for performance evaluation. Theor. Comput. Sci. 274(1–2), 43–87 (2002). https://doi.org/10.1016/S0304-3975(00)00305-4

    MathSciNet  Article  MATH  Google Scholar 

  35. 158.

    Howard, R.A., Matheson, J.E.: Influence diagrams. Decis. Anal. 2(3), 127–143 (2005). https://doi.org/10.1287/deca.1050.0020

    Article  Google Scholar 

  36. 159.

    Humphrey, W.S.: Characterizing the software process: a maturity framework. IEEE Softw. 5(2), 73–79 (1998). https://doi.org/10.1109/52.2014

    MathSciNet  Article  Google Scholar 

  37. 160.

    Immonen, A., Niemelä, E.: Survey of reliability and availability prediction methods from the viewpoint of software architecture. Softw. Syst. Model. 7(1), 49–65 (2008). https://doi.org/10.1007/s10270-006-0040-x

    Article  Google Scholar 

  38. 161.

    Islam, F., Petriu, D.C., Woodside, C.M.: Simplifying layered queuing network models. In: Proceeding of EPEW’15, Lecture Notes in Computer Science, vol. 9272, pp. 65–79. Springer (2015). https://doi.org/10.1007/978-3-319-23267-6_5

  39. 162.

    ISO 9000:2015: Quality management systems—Fundamentals and vocabulary (2015). https://www.iso.org/obp/ui/#iso:std:iso:9000:ed-4:v1:en

  40. 163.

    JCGM 100:2008: Evaluation of measurement data—Guide to the expression of uncertainty in measurement (GUM). Joint Committee for Guides in Metrology (2008). http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

  41. 164.

    Jøsang, A.: Subjective Logic—A Formalism for Reasoning Under Uncertainty. Artificial Intelligence: Foundations, Theory, and Algorithms. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-42337-1

  42. 165.

    Karkhanis, P., van den Brand, M.G.J., Rajkarnikar, S.: Defining the C-ITS reference architecture. In: ICSA’18 Companion, pp. 148–151. IEEE Computer Society (2018). https://doi.org/10.1109/ICSA-C.2018.00044

  43. 166.

    Kitchenham, B.: Procedures for performing systematic reviews. Technical Report TR/SE-0401, Keele University (2004). http://www.inf.ufsc.br/~aldo.vw/kitchenham.pdf

  44. 167.

    Kiureghian, A.D., Ditlevsen, O.: Aleatory or epistemic? Does it matter? Struct. Saf. 31(2), 105–112 (2009)

    Article  Google Scholar 

  45. 168.

    Koziolek, H.: Performance evaluation of component-based software systems: a survey. Perform. Eval. 67(8), 634–658 (2010). https://doi.org/10.1016/j.peva.2009.07.007

    Article  Google Scholar 

  46. 169.

    Kwon, W.T., Park, N.C., Jung, S.H.J., Kim, T.G.: Fuzzy-DEVS formalism: concepts, realization and applications. In: Proceedings of AIS’96, pp. 227—234 (1996)

  47. 170.

    van Lamsweerde, A.: Requirements Engineering—From System Goals to UML Models to Software Specifications. Wiley, Chichester (2009)

    Google Scholar 

  48. 171.

    Lano, K., Rahimi, S.K., Tehrani, S.Y., Sharbaf, M.: A survey of model transformation design patterns in practice. J. Syst. Softw. 140, 48–73 (2018). https://doi.org/10.1016/j.jss.2018.03.001

    Article  Google Scholar 

  49. 172.

    Larsen, K.G., Thomsen, B.: A modal process logic. In: Proceedings of LICS’88, pp. 203–210. IEEE Computer Society (1988). https://doi.org/10.1109/LICS.1988.5119

  50. 173.

    Lebigot, E.O.: Uncertainties: a Python package for calculations with uncertainties (2017). https://pythonhosted.org/uncertainties/

  51. 174.

    Lee, E.A., Sirjani, M.: What good are models? In: Proceedings of FACS’18, LNCS, vol. 11222, pp. 3–31. Springer (2018). https://doi.org/10.1007/978-3-030-02146-7_1

  52. 175.

    Li, L., Wang, H., Li, J., Gao, H.: A survey of uncertain data management. Front. Comput. Sci. 14(1), 162–190 (2020). https://doi.org/10.1007/s11704-017-7063-z

    Article  Google Scholar 

  53. 176.

    Liu, B.: Uncertainty Theory, 5 edn. Springer, Berlin (2018). http://orsc.edu.cn/liu/ut.pdf

  54. 177.

    Looney, C.G.: Fuzzy petri nets for rule-based decision-making. IEEE Trans. Syst. Man Cybernet. 18(1), 178–183 (1988). https://doi.org/10.1109/21.87067

    Article  Google Scholar 

  55. 178.

    Ma, Z.M., Yan, L.: A literature overview of fuzzy conceptual data modeling. J. Inf. Sci. Eng. 26(2), 427–441 (2010)

    Google Scholar 

  56. 179.

    Maccaferri, L.: Using Zotero to convert Springer Link CSV search result to BibTex format (2017). https://www.leniel.net/2017/06/using-zotero-to-convert-springerlink-full-csv-search-result-to-bibtex-format.html

  57. 180.

    Mahdavi-Hezavehi, S., Avgeriou, P., Weyns, D.: A Classification Framework of Uncertainty in Architecture-Based Self-Adaptive Systems With Multiple Quality Requirements, Chap. 3, pp. 45–47. Morgan Kaufmann (2017). B978-0-12-802855-1.00003-4

  58. 181.

    Manzano, M.A., de Felipe-Rodríguez, H., Gago-Gómez, L.: DICTOMAGRED: Diccionario de Toponimia Magrebí (2018). https://dictomagred.usal.es/

  59. 182.

    Marsan, M.A., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley, Hoboken (1995)

    MATH  Google Scholar 

  60. 183.

    Marsan, M.A., Conte, G., Balbo, G.: A class of generalized stochastic petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comput. Syst. 2(2), 93–122 (1984). https://doi.org/10.1145/190.191

    Article  Google Scholar 

  61. 184.

    ickMoon, S., Lee, K.H., Lee, D.: Fuzzy branching temporal logic. IEEE Trans. Syst. Man Cybernet. Part B Cybernet. 34(2), 1045–1055 (2004). https://doi.org/10.1109/TSMCB.2003.819485

    Article  Google Scholar 

  62. 185.

    Moreno, G.A., Cámara, J., Garlan, D., Klein, M.: Uncertainty reduction in self-adaptive systems. In: Andersson, J., Weyns, D. (eds.) Proceedings of SEAMS@ICSE’18, pp. 51–57. ACM (2018). https://doi.org/10.1145/3194133.3194144

  63. 186.

    Moreno, N., Bertoa, M.F., Burgueño, L., Vallecillo, A.: Managing measurement and occurrence uncertainty in complex event processing systems. IEEE Access 7, 88026–88048 (2019). https://doi.org/10.1109/ACCESS.2019.2923953

    Article  Google Scholar 

  64. 187.

    Mosterman, P.J., Zander, J.: Industry 4.0 as a cyber-physical system study. Softw. Syst. Model. 15(1), 17–29 (2016). https://doi.org/10.1007/s10270-015-0493-x

    Article  Google Scholar 

  65. 188.

    Novák, P.: Probabilistic behavioural state machines. In: Proceedings of ProMAS’09, LNCS, vol. 5919, pp. 67–81. Springer (2009). https://doi.org/10.1007/978-3-642-14843-9_5

  66. 189.

    Oberkampf, W.L., DeLand, S.M., Rutherford, B.M., Diegert, K.V., Alvin, K.F.: Error and uncertainty in modeling and simulation. Reliab. Eng. Syst. Saf. 75(3), 333–357 (2002). https://doi.org/10.1016/S0951-8320(01)00120-X

    Article  Google Scholar 

  67. 190.

    Object Management Group: UML Profile for Schedulability, Performance and Time. Version 1.1 (2005). OMG Document formal/05-01-02

  68. 191.

    Object Management Group: UML Testing Profile, version 1.2 (2013). OMG Document formal/13-04-03

  69. 192.

    Object Management Group: Interaction Flow Modeling Language (IFML), version 1.0 (2015). OMG Document formal/15-02-05

  70. 193.

    Object Management Group: Precise Semantics for Uncertainty Modeling (PSUM) RFP (2017). OMG Document ad/2017-12-1

  71. 194.

    Object Management Group: Semantics Of A Foundational Subset For Executable UML Models (FUML), version 1.4 (2018). OMG Document formal/18-12-01

  72. 195.

    Othman, N.A., Eldin, A.S., Zanfaly, D.S.E.: Handling uncertainty in database: an introduction and brief survey. Comput. Inf. Sci. 8(3), 119–133 (2015). https://doi.org/10.5539/cis.v8n3p119

    Article  Google Scholar 

  73. 196.

    Pearl, J.: A probabilistic calculus of actions. In: Proceedings of the Tenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI’94), pp. 454–462. Morgan Kaufmann (1994)

  74. 197.

    Pearl, J.: Causality: Models, reasoning and inference. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  75. 198.

    Pearl, J., Mackenzie, D.: The Book of Why: The New Science of Cause and Effect. Basic Books, New York (2018)

    MATH  Google Scholar 

  76. 199.

    Perez-Palacin, D., Mirandola, R.: Uncertainties in the modeling of self-adaptive systems: a taxonomy and an example of availability evaluation. In: Proceedings of ICPE’14, pp. 3–14. ACM (2014). https://doi.org/10.1145/2568088.2568095

  77. 200.

    Pivert, O., Prade, H.: Handling uncertainty in relational databases with possibility theory—a survey of different modelings. In: Proceedings of SUM’18, LNCS, vol. 11142, pp. 396–404. Springer (2018). https://doi.org/10.1007/978-3-030-00461-3_30

  78. 201.

    Ramirez, A.J., Jensen, A.C., Cheng, B.H.C.: A taxonomy of uncertainty for dynamically adaptive systems. In: Proceedings of SEAMS’12, pp. 99–108. IEEE Computer Society (2012). https://doi.org/10.1109/SEAMS.2012.6224396

  79. 202.

    Rausand, M.: Risk Assessment: Theory, Methods, and Applications. Wiley, Hoboken (2013)

    MATH  Google Scholar 

  80. 203.

    Refsdal, A.: Specifying computer systems with probabilistic sequence diagrams. Ph.D. thesis, University of Oslo, Norway (2008). https://www.duo.uio.no/handle/10852/9873

  81. 204.

    Rinderknecht, S.L., Borsuk, M.E., Reichert, P.: Bridging uncertain and ambiguous knowledge with imprecise probabilities. Environ. Model. Softw. 36, 122–130 (2012). https://doi.org/10.1016/j.envsoft.2011.07.022

    Article  Google Scholar 

  82. 205.

    Russell, S.J., Norvig, P.: Artificial Intelligence, A Modern Approach, 3rd edn. Prentice Hall, Upper Saddle River (2010)

    MATH  Google Scholar 

  83. 206.

    Sadegh-Zadeh, K.: Fuzzy deontics. In: Soft Computing in Humanities and Social Sciences, Studies in Fuzziness and Soft Computing, vol. 273, pp. 141–156. Springer (2012). https://doi.org/10.1007/978-3-642-24672-2_7

  84. 207.

    Salih, A.M., Omar, M., Yasin, A.: Understanding uncertainty of software requirements engineering: a systematic literature review protocol. In: Proceeding of APRES’17, Communications in Computer and Information Science, vol. 809, pp. 164–171. Springer (2017). https://doi.org/10.1007/978-981-10-7796-8_13

  85. 208.

    Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis: The Primer. Wiley, Hoboken (2008). https://doi.org/10.1002/9780470725184

  86. 209.

    Saoud, Z., Faci, N., Maamar, Z., Benslimane, D.: A fuzzy-based credibility model to assess Web services trust under uncertainty. J. Syst. Softw. 122, 496–506 (2016). https://doi.org/10.1016/j.jss.2015.09.040

    Article  Google Scholar 

  87. 210.

    Seely, A.J., Macklem, P.T.: Complex systems and the technology of variability analysis. Crit. Care 8, 367–384 (2004). https://doi.org/10.1186/cc2948

    Article  Google Scholar 

  88. 211.

    Selic, B.: Beyond mere logic—a vision of modeling languages for the 21st century. In: Proceedings of MODELSWARD 2015 and PECCS 2015, pp. IS–5. SciTePress (2015). http://cescit2015.um.si/Presentations/KN_Selic.pdf

  89. 212.

    Senaratne, H., Gerharz, L., Pebesma, E., Schwering, A.: Usability of spatio-temporal uncertainty visualisation methods. In: Bridging the Geographic Information Sciences. Proceedings of AGILE’12, Lecture Notes in Geoinformation and Cartography, pp. 3–23. Springer (2012). https://doi.org/10.1007/978-3-642-29063-3_1

  90. 213.

    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    Book  Google Scholar 

  91. 214.

    Shokravi, S., Smith, A.J.R., Burvill, C.R.: Industrial environmental performance evaluation: a Markov-based model considering data uncertainty. Environ. Model. Softw. 60, 1–17 (2014). https://doi.org/10.1016/j.envsoft.2014.05.024

    Article  Google Scholar 

  92. 215.

    da Silva Hack, P., ten Caten, C.S.: Measurement uncertainty: literature review and research trends. IEEE Trans. Instrum. Meas. 61(8), 2116–2124 (2012). https://doi.org/10.1109/TIM.2012.2193694

    Article  Google Scholar 

  93. 216.

    Sinnema, M., Deelstra, S.: Classifying variability modeling techniques. Inf. Softw. Technol. 49(7), 717–739 (2007). https://doi.org/10.1016/j.infsof.2006.08.001

    Article  Google Scholar 

  94. 217.

    Smith, C.U.: Performance Engineering of Software Systems. Addison-Wesley, Boston (1990)

    Google Scholar 

  95. 218.

    Thornton, A., Lee, P.: Publication bias in meta-analysis: its causes and consequences. J. Clin. Epidemiol. 53(2), 207–216 (2000). https://doi.org/10.1016/S0895-4356(99)00161-4

    Article  Google Scholar 

  96. 219.

    Thunnissen, D.P.: Uncertainty classification for the design and development of complex systems. In: Proceedings of the 3rd Annual Predictive Methods Conference, Veros Software (2003). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.133

  97. 220.

    Troya, J., Moreno, N., Bertoa, M.F., Vallecillo, A.: Representing uncertainty in software models: a survey—companion website (2020). http://atenea.lcc.uma.es/projects/UncertaintySurvey.html

  98. 221.

    Tumeo, M.A.: The meaning of stochasticity, randomness and uncertainty in environmental modeling. In: Stochastic and Statistical Methods in Hydrology and Environmental Engineering, vol. 2, pp. 33–38. Springer, Dordrecht (1994). https://doi.org/10.1007/978-94-011-1072-3_3

  99. 222.

    Vanherpen, K., Denil, J., Meulenaere, P.D., Vangheluwe, H.: Design-space exploration in MDE: an initial pattern catalogue. In: Proceedings of CMSEBA@MODELS’14, CEUR Workshop Proceedings, vol. 1340, pp. 42–51. CEUR-WS.org (2014). http://ceur-ws.org/Vol-1340/paper6.pdf

  100. 223.

    Walker, W., Harremoës, P., Rotmans, J., van der Sluijs, J., van Asselt, M., Janssen, P., Krayer von Krauss, M.: Defining uncertainty: a conceptual basis for uncertainty management in model-based decision support. Integr. Assess. 4(1), 5–17 (2003). https://doi.org/10.1076/iaij.4.1.5.16466

  101. 224.

    Wang, Y., Li, X., Li, X., Wang, Y.: A survey of queries over uncertain data. Knowl. Inf. Syst. 37(3), 485–530 (2013). https://doi.org/10.1007/s10115-013-0638-6

    Article  Google Scholar 

  102. 225.

    Wang, Y.H., Cao, K., Zhang, X.M.: Complex event processing over distributed probabilistic event streams. Comput. Math. Appl. 66(10), 1808–1821 (2013)

    Article  Google Scholar 

  103. 226.

    Webster, J., Watson, R.T.: Analyzing the past to prepare for the future: writing a literature review. MIS Q. 26(2), xii–xxiii (2002)

  104. 227.

    Wohlin, C.: Guidelines for snowballing in systematic literature studies and a replication in software engineering. In: Proceedings of EASE’14, pp. 38:1–38:10. ACM (2014). https://doi.org/10.1145/2601248.2601268

  105. 228.

    Wohlin, C., Runeson, P., Höst, M., Ohlsson, M.C., Regnell, B., Wesslén, A.: Experimentation in Software Engineering. Springer, Berlin (2012)

    Book  Google Scholar 

  106. 229.

    Wolny, S., Mazak, A., Carpella, C., Geist, V., Wimmer, M.: Thirteen years of SysML: a systematic mapping study. Softw. Syst. Model. 19(1), 111–169 (2020). https://doi.org/10.1007/s10270-019-00735-y

    Article  Google Scholar 

  107. 230.

    Woltzenlogel Paleo, B.: An expressive probabilistic temporal logic. CoRR arXiv:abs/1603.07453 (2016). http://arxiv.org/abs/1603.07453

  108. 231.

    Wong, S.K.M., Butz, C.J.: Rough sets for uncertainty reasoning. In: Proceedings of RSCTC’00, LNCS, vol. 2005, pp. 511–518. Springer (2000). https://doi.org/10.1007/3-540-45554-X_63

  109. 232.

    Wortmann, A., Barais, O., Combemale, B., Wimmer, M.: Modeling languages in industry 4.0: an extended systematic mapping study. Softw. Syst. Model. 19(1), 67–94 (2020)

    Article  Google Scholar 

  110. 233.

    Zimmermann, H.J.: Fuzzy Set Theory—and Its Applications. Springer Science+Business Media, Berlin (2001)

    Book  Google Scholar 

  111. 234.

    Zvieli, A., Chen, P.P.: Entity-relationship modeling and fuzzy databases. In: Proceedings of ICDE’86, pp. 320–327. IEEE Computer Society (1986). https://doi.org/10.1109/ICDE.1986.7266236

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Acknowledgements

We would like to thank the reviewers of the paper for their insightful comments and very valuable suggestions, which helped us significantly to improve this work. Many thanks also to the authors of the cited papers and to other members of the community who kindly provided comments and feedback on earlier drafts of this paper. This work is partially supported by the European Commission (FEDER) and the Spanish Government under projects APOLO (US-1264651), HORATIO (RTI2018-101204-B-C21), EKIPMENT-PLUS (P18-FR-2895) and COSCA (PGC2018-094905-B-I00).

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Troya, J., Moreno, N., Bertoa, M.F. et al. Uncertainty representation in software models: a survey. Softw Syst Model 20, 1183–1213 (2021). https://doi.org/10.1007/s10270-020-00842-1

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Keywords

  • Software models
  • Uncertainty
  • Modeling languages
  • UML
  • Systematic literature review