Application of a fuzzy unit hypercube in cardiovascular risk classification

  • Geoffrey O. BariniEmail author
  • Livingstone M. Ngoo
  • Ronald W. Mwangi
Methodologies and Application


Most standard cardiovascular disease (CVD) risk assessment models are based on traditional quantitative approaches. Such models oversimplify complex interactions emanating from the imprecise nature of CVD risk factors. As such, approaches that can handle uncertainty due to imprecision need to be explored. This study proposes a cardiovascular risk classification model based on the geometry of fuzzy sets, which allows for a multidimensional display of qualitative properties associated with risk attributes—that are defined in a fuzzy sense. Within this structure, a risk concept (which defines the degree of risk severity) is simply a continuum of points of the hypercube. Consequently, an individual’s risk status would naturally be represented by an ordered fuzzy within the continuum. This representation forms an excellent comparative framework through measures of similarity where an individual’s relative position in the continuum can be given as degrees of compatibility with the underlying risk concepts.


Fuzzy hypercube Similarity measure Risk continuum 



This work was supported by the Pan African University, Institute of Basic Sciences, Technology and Innovation under the Commission of the African Union.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


  1. Acs A, Ludwig C, Bereza B, Einarson T, Panton U (2017) Economic burden of cardiovascular disease in type 2 diabetes: a systematic review. Value Health 20(9):A476–A477CrossRefGoogle Scholar
  2. Alqudah AM (2017) Fuzzy expert system for coronary heart disease diagnosis in Jordan. Health Technol 7(2–3):215–222CrossRefGoogle Scholar
  3. Anderson KM, Odell PM, Wilson PW, Kannel WB (1991) Cardiovascular disease risk profiles. Am Heart J 121(1):293–298CrossRefGoogle Scholar
  4. Anooj P (2012) Clinical decision support system: risk level prediction of heart disease using weighted fuzzy rules. J King Saud Univ Comput Inf Sci 24(1):27–40Google Scholar
  5. Barro S, Marín R (2013) Fuzzy logic in medicine, vol 83. Physica-Verlag, HeidelbergzbMATHGoogle Scholar
  6. Berry JD, Dyer A, Cai X, Garside DB, Ning H, Thomas A, Greenland P, Van Horn L, Tracy RP, Lloyd-Jones DM (2012) Lifetime risks of cardiovascular disease. N Engl J Med 366(4):321–329CrossRefGoogle Scholar
  7. Boon N, Boyle R, Bradbury K, Buckley J, Connolly S, Craig S, Deanfield J, Doherty P, Feher M, Fox K et al (2014) Joint British Societies’ consensus recommendations for the prevention of cardiovascular disease (JBS3). Heart 100(Suppl 2):ii1–ii67CrossRefGoogle Scholar
  8. Buede DM (1994) Examination of the fuzzy subsethood theorem for data fusion. In: Multisensor fusion and integration for intelligent systems, 1994. IEEE international conference on MFI’94, IEEE, pp 430–434Google Scholar
  9. Ephzibah E (2011) A hybrid genetic-fuzzy expert system for effective heart disease diagnosis. In: Wyld DC, Wozniak M, Chaki N, Meghanathan N, Nagamalai D (eds) Advances in computing and information technology. Springer, Berlin, pp 115–121CrossRefGoogle Scholar
  10. Go AS, Chertow GM, Fan D, McCulloch CE, Hsu Cy (2004) Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization. N Engl J Med 351(13):1296–1305CrossRefGoogle Scholar
  11. Grossi E (2006) How artificial intelligence tools can be used to assess individual patient risk in cardiovascular disease: problems with the current methods. BMC Cardiovasc Disord 6(1):20MathSciNetCrossRefGoogle Scholar
  12. Helgason CM, Jobe TH (1998) The fuzzy cube and causal efficacy: representation of concomitant mechanisms in stroke. Neural Netw 11(3):549–555CrossRefGoogle Scholar
  13. Helgason CM, Watkins FA, Jobe TH (2002) Measurable differences between sequential and parallel diagnostic decision processes for determining stroke subtype: a representation of interacting pathologies. Thromb Haemost 88(02):210–212Google Scholar
  14. Kahtan H, Zamli KZ, Fatthi WNAWA, Abdullah A, Abdulleteef M, Kamarulzaman NS (2018) Heart disease diagnosis system using fuzzy logic. In: Proceedings of the 2018 7th international conference on software and computer applications, ACM, pp 297–301Google Scholar
  15. Kasbe T, Pippal RS (2017) Design of heart disease diagnosis system using fuzzy logic. In: 2017 international conference on energy, communication, data analytics and soft computing (ICECDS), IEEE, pp 3183–3187Google Scholar
  16. Kim J, Lee J, Lee Y (2015) Data-mining-based coronary heart disease risk prediction model using fuzzy logic and decision tree. Healthc Inform Res 21(3):167–174CrossRefGoogle Scholar
  17. Kosko B (1990) Fuzziness vs. probability. Int J General Syst 17(2–3):211–240CrossRefzbMATHGoogle Scholar
  18. Krittanawong C, Zhang H, Wang Z, Aydar M, Kitai T (2017) Artificial intelligence in precision cardiovascular medicine. J Am Coll Cardiol 69(21):2657–2664CrossRefGoogle Scholar
  19. Leal J, Luengo-Fernández R, Gray A, Petersen S, Rayner M (2006) Economic burden of cardiovascular diseases in the enlarged european union. Eur Heart J 27(13):1610–1619CrossRefGoogle Scholar
  20. Lewis M, Lawry J (2016) Hierarchical conceptual spaces for concept combination. Artif Intell 237:204–227MathSciNetCrossRefzbMATHGoogle Scholar
  21. Mozaffarian D, Benjamin EJ, Go AS, Arnett DK, Blaha MJ, Cushman M, Das SR, de Ferranti S, Després JP, Fullerton HJ et al (2015) Heart disease and stroke statistics—2016 update: a report from the American heart association. Circulation 133(4):e38–e360. Google Scholar
  22. Narayan KV, Ali MK, Koplan JP (2010) Global noncommunicable diseases—where worlds meet. N Engl J Med 363(13):1196–1198CrossRefGoogle Scholar
  23. Nieto JJ, Torres A (2003) Midpoints for fuzzy sets and their application in medicine. Artif Intell Med 27(1):81–101CrossRefGoogle Scholar
  24. O’Donnell CJ, Elosua R (2008) Cardiovascular risk factors. Insights from framingham heart study. Revista Espanola de Cardiologia (English Edition) 61(3):299–310Google Scholar
  25. O’gara PT, Kushner FG, Ascheim DD, Casey DE, Chung MK, De Lemos JA, Ettinger SM, Fang JC, Fesmire FM, Franklin BA et al (2013) 2013 ACCF/AHA guideline for the management of st-elevation myocardial infarction: executive summary: a report of the American college of cardiology foundation/American heart association task force on practice guidelines. J Am Coll Cardiol 61(4):485–510CrossRefGoogle Scholar
  26. Rajeswari K, Vaithiyanathan V (2011) Heart disease diagnosis: an efficient decision support system based on fuzzy logic and genetic algorithm. Int J Decis Sci Risk Manag 3(1–2):81–97Google Scholar
  27. Rickard JT (2006) A concept geometry for conceptual spaces. Fuzzy Optim Decis Mak 5(4):311–329MathSciNetCrossRefzbMATHGoogle Scholar
  28. Ross TJ (2009) Fuzzy logic with engineering applications. Wiley, HobokenGoogle Scholar
  29. Roth GA, Johnson C, Abajobir A, Abd-Allah F, Abera SF, Abyu G, Ahmed M, Aksut B, Alam T, Alam K et al (2017) Global, regional, and national burden of cardiovascular diseases for 10 causes, 1990 to 2015. J Am Coll Cardiol 70(1):1–25CrossRefGoogle Scholar
  30. Sadegh-Zadeh K (1999) Fundamentals of clinical methodology: 3. Nosology. Artif Intell Med 17(1):87–108CrossRefGoogle Scholar
  31. Sadegh-Zadeh K et al (2012) Handbook of analytic philosophy of medicine. Springer, DordrechtCrossRefGoogle Scholar
  32. Savinov AA (1999) Application of multi-dimensional fuzzy analysis to decision making. In: Roy R, Furuhashi T, Chawdhry PK (eds) Advances in soft computing. Springer, London, pp 301–314CrossRefGoogle Scholar
  33. Stamler J, Vaccaro O, Neaton JD, Wentworth D, Group MRFITR et al (1993) Diabetes, other risk factors, and 12-yr cardiovascular mortality for men screened in the multiple risk factor intervention trial. Diabetes Care 16(2):434–444Google Scholar
  34. Ventola CL (2014) Mobile devices and apps for health care professionals: uses and benefits. Pharm Ther 39(5):356Google Scholar
  35. Vijaya K, Khanna Nehemiah H, Kannan A, Bhuvaneswari N (2010) Fuzzy neuro genetic approach for predicting the risk of cardiovascular diseases. Int J Data Min Model Manag 2(4):388–402Google Scholar
  36. Wilson PW, D’Agostino RB, Levy D, Belanger AM, Silbershatz H, Kannel WB (1998) Prediction of coronary heart disease using risk factor categories. Circulation 97(18):1837–1847CrossRefGoogle Scholar
  37. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefzbMATHGoogle Scholar
  38. Zahan S, Bogdan R, Capalneanu R (2000) Fuzzy expert system for cardiovascular disease diagnosis-tests and performance evaluation. In: Proceedings of the 5th seminar on neural network applications in electrical engineering, 2000. NEUREL 2000. IEEE, pp 65–68Google Scholar
  39. Zhang XS, Leu FY, Yang CW, Lai LS (2018) Healthcare-based on cloud electrocardiogram system: a medical center experience in middle Taiwan. J Med Syst 42(3):39CrossRefGoogle Scholar
  40. Zhao J, Bose BK (2002) Evaluation of membership functions for fuzzy logic controlled induction motor drive. In: IECON 02 IEEE 2002 28th annual conference of the industrial electronics society, IEEE, vol 1, pp 229–234Google Scholar
  41. Zhiqiang G, Lingsong H, Hang T, Cong L (2015) A cloud computing based mobile healthcare service system. In: 2015 IEEE 3rd international conference on smart instrumentation, measurement and applications (ICSIMA), IEEE, pp 1–6Google Scholar
  42. Zimmermann HJ (2011) Fuzzy set theory—and its applications. Springer, New YorkGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Basic Sciences, Technology and InnovationPan African UniversityNairobiKenya
  2. 2.Department of Pure and Applied MathematicsJomo Kenyatta University of Agriculture and TechnologyNairobiKenya
  3. 3.Department of Electrical and Telecommunication EngineeringMultimedia University of KenyaNairobiKenya
  4. 4.Department of ComputingJomo Kenyatta University of Agriculture and TechnologyNairobiKenya

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