Using Phi Coefficient to Interpret Results Obtained by InterCriteria Analysis

  • Lyudmila Todorova
  • Peter VassilevEmail author
  • Jivko Surchev
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


The authors propose an algorithm for assessment of the estimates of “correspondence” and “opposition” obtained by InterCriteria Analysis (ICA) in the form of intuitionistic fuzzy vector pairs. For this aim the modified Pearson coefficient of Karl Pearson, called \(\varphi \) coefficient (“mean square contingency coefficient”). The algorithm is applied on real data from neurosurgery. The statistical significance of the relations between the considered criteria is verified by data found in literature. The authors believe this approach for data exploration may prove useful in many areas.


InterCriteria analysis Pearson phi Correlation Intuitionistic fuzzy vector pairs 



The first two authors are grateful for the support provided by Grant DFNI-I-02-5 “InterCriteria Analysis—A New Approach to Decision Making” of the Bulgarian National Science Fund.


  1. 1.
    Galton, F.: Co-relations and their measurement, chiefly from anthropometric data. Proc. Roy. Soc. Lond. 45, 135–145 (1888)CrossRefGoogle Scholar
  2. 2.
    Atanassov, K., Mavrov, D., Atanassova, V.: Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Issues IFSs GNs 11, 1–8 (2014)Google Scholar
  3. 3.
    Atanassov, K.: On index matrices, part 1: standard cases. Adv. Stud. Contemp. Math. 20(2), 291–302 (2010)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes IFS 19(3), 1–13 (2013)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Di Rocco, F., Garnett, M., Roujeau, T., Puget, S., Renier, D., Zerah, M., Sainte-Rose, C.: Neurosurgery, European Manual of Medicine, Hydrocephalus, vol. 7, pp. 539–543. Springer (2010)Google Scholar
  6. 6.
    Hoffman, H.J., Soloniuk, D., Humphreys, R.P., et al.: A concerted effort to prevent shunt infection. In: Matsumoto, S., Tamaki, N. (eds.) Hydrocephalus: Pathogenesis and Treatment, pp. 510–514. Springer, New York (1991)Google Scholar
  7. 7.
    Schreffler, R.T., Schreffler, A.J., Wittler, R.R.: Treatment of cerebrospinal fluid shunt infections: a decision analysis. Pediatr. Infect. Dis. J. 21, 632–636 (2002)CrossRefGoogle Scholar
  8. 8.
    Walters, B.C., Hoffman, H.J., Hendrick, E.B., Humphreys, R.P.: Cerebrospinal fluid shunt infection. Influences on initial management and subsequent outcome. J. Neurosurg. 60(5), 1014–1021 (1984)CrossRefGoogle Scholar
  9. 9.
    Piatt Jr, J.H., Carlson, C.V.: A search for determinants of cerebrospinal fluid shunt survival: Retrospective analysis of a 14-year institutional experience. Pediatr. Neurosurg. 19(5), 233–242 (1993)CrossRefGoogle Scholar
  10. 10.
    Tuli, S., Drake, J., Lawless, J., Wigg, M., Lamberti-Pasculli, M.: Risk factors for repeated cerebrospinal shunt failures in pediatric patients with hydrocephalus. J. Neurosurg. 92, 31–38 (2000)Google Scholar
  11. 11.
    Weprin, B.E., Swift, D.M.: Complications of ventricular shunts. Tech. Neurosurg. 7(3), 224–242 (2002)CrossRefGoogle Scholar
  12. 12.
    Pearson, K.: Notes on regression and inheritance in the case of two parents. Proc. R. Soc. Lond. 58, 240242 (1895)Google Scholar
  13. 13.
    Kendall, M.: A new measure of rank correlation. Biometrika 30(12), 81–89 (1938)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Spearman, C.: The proof and measurement of correlation between two things. Am. J. Psychol. 15, 72101 (1904)Google Scholar
  15. 15.
    Korinth, M.C., Weinzierl, M.R., Gilsbach, M.: Experience with a new concept to lower non-infectious complications in infants with programmable shunts. Eur. J. Pediatr. Surg. 13, 81–86 (2003)CrossRefGoogle Scholar
  16. 16.
    Shannon, C.N., Acakpo-Satchivi, L., Kirby, R.S., Franklin, F.A., Wellons, J.C., Ventriculoperitoneal shunt failure: an institutional review of 2-year survival rates. Child’s Nerv. Syst. 1–7, (2012)Google Scholar
  17. 17.
    Wu, Y., Green, N.L., Wrensch, M.R., Zhao, S., Gupta, N.: Ventriculoperitoneal shunt complications in California: 1990 to 2000. Neurosurgery 61(3), 557–562 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Lyudmila Todorova
    • 1
  • Peter Vassilev
    • 1
    Email author
  • Jivko Surchev
    • 2
  1. 1.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of NeurosurgeryMedical University SofiaSofiaBulgaria

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