Strengthening and Weakening Members of a Network

  • John N. Mordeson
  • Sunil Mathew
  • Davender S. Malik
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 365)


In 1965, Lotfi A. Zadeh (Fuzzy sets. Inf. Control 8, 338–353, 1965) [34] introduced a new type of set called a fuzzy set and a new logic later known as fuzzy logic. Instead of YES or NO, regarding the existence of an element in a set, he used the degree of membership, which allows an element to exist in a set with a partial grade of membership. The applications of fuzzy logic are profound and widespread.


  1. 1.
    M. Akram, N.O. Alshehri, Intuitionistic fuzzy cycles and intuitionistic fuzzy trees. Sci. World J. ID 305836, 1–11 (2014). (Hindawi Publishing Corporation)Google Scholar
  2. 2.
    M. Akram, B. Davvaz, Strong intuitionistic fuzzy graphs. Filomat 26, 177–195 (2012)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    M. Akram, M.G. Karunambigai, O.K. Kalaivani, Some metric aspects of intuitionistic fuzzy graphs. World Appl. Ser. J. 17, 1789–1801 (2012)Google Scholar
  4. 4.
    K.T. Atanassov, On intuitionistic fuzzy graphs and intuitionistic fuzzy relations, in Proceedings of the 6th IFSA World Congress vol. 1 (San Paulo, Brazil, 1995), pp. 551–554Google Scholar
  5. 5.
    K.T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefMATHGoogle Scholar
  6. 6.
    K.T. Atanassov, A. Shannon, On a generalization of intuitionistic fuzzy graphs. Notes Intuit. Fuzzy Sets 12, 24–29 (2006)Google Scholar
  7. 7.
    K.R. Bhutani, J.N. Mordeson, P.K. Saha, \((s,t]\) -fuzzy graphs, in JCIS Proceedings (2005), pp. 37–40Google Scholar
  8. 8.
    K.R. Bhutani, A. Rosenfeld, Fuzzy end nodes in fuzzy graphs. Inf. Sci. 152, 323–326 (2003)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    K.R. Bhutani, J.N. Mordeson, A. Rosenfeld, On degrees of end nodes and cut nodes in fuzzy graphs. Iranian J. Fuzzy Syst. 1, 57–64 (2004)MathSciNetMATHGoogle Scholar
  10. 10.
    C. Caniglia, B. Cousino, S.-C. Cheng, D.S. Malik, J.N. Mordeson, Intuitionistic fuzzy graphs: weakening and strengthening members of a group. J. Fuzzy Math. 24, 87–102 (2016)MATHGoogle Scholar
  11. 11.
    Central Intelligence Agency, Field Listing: Trafficking in Persons (2014).
  12. 12.
    P. Chountas, A. Shannon, P. Rangasamy, K. Atassov, On intuitionistic fuzzy trees and their index matrix interpretation. Notes Intuit. Fuzzy Sets 15, 52–56 (2009)MATHGoogle Scholar
  13. 13.
    U.S. Department of State, Diplomacy in Action, Trafficking in Persons Report 2013: Tier Placements.
  14. 14.
    F. Harary, R.Z. Norman, Graph Theory as a Mathematical Model in Social Science, Ann Arbor, Mich.: Institute for Social Research, 1953)Google Scholar
  15. 15.
    F. Harary, R.Z. Norman, D. Cartwright, Introduction to digraph theory for social scientists, in Process of Publication Google Scholar
  16. 16.
    F. Harary, Graph theoretic methods in the management sciences. Manag. Sci. 5, 387–403 (1959)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    F. Harary, I.C. Ross, The number of complete cycles in a communication network. J. Soc. Psychol. 40, 329–332 (1953)CrossRefGoogle Scholar
  18. 18.
    F. Harary, I.C. Ross, A procedure for clique detention using the group matrix. Sociometry 20, 205–215 (1957)MathSciNetCrossRefGoogle Scholar
  19. 19.
    A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, vol. 1 (Academic Press, New York, 1975)MATHGoogle Scholar
  20. 20.
    G.J. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice Hall PTR, Upper Saddle River, 1995)MATHGoogle Scholar
  21. 21.
    P.P. Ming, L.Y. Ming, Fuzzy topology I: neighborhood structure of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl. 76, 571–599 (1980)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    J.N. Mordeson, P.S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs. Studies in Fuzziness and Soft Computing, vol. 46 (Physica-Verlag, Heidelberg, 2000)Google Scholar
  23. 23.
    J.N. Mordeson, D.S. Malik, C.D. Richards, J.A. Trebbian, M.A. Boyce, M.P. Byrne, B.J. Cousino, Fuzzy graphs and complementary fuzzy graphs. J. Fuzzy Math. 24, 271–288 (2016)MATHGoogle Scholar
  24. 24.
    R. Parvathi, M.G. Karunambigigai, Intuitionistic fuzzy graphs. Adv. Soft Comput. 38, 139–159 (2006)Google Scholar
  25. 25.
    G. Pasi, R. Yager, K. Atanassov, Intuitionistic fuzzy graph interpretations of multi-person multi-critera decision making: generalized net approach, in Proceedings of the 2nd International IEEE Conference in Intelligent Systems (2004), pp. 434–439Google Scholar
  26. 26.
    D. Rosenblatt, On linear models and the graphs of Minkowski -Leontief matrices. Econometrica 25, 325–338 (1975)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    A. Rosenfeld, Fuzzy graphs, in Fuzzy Sets and Their Applications, ed. by L.A. Zadeh, K.S. Fu, M. Shimura (Academic Press, 1975), pp. 77–95Google Scholar
  28. 28.
    I.C. Ross, F. Harary, On the determination of redundancies in sociometric chains. Psychometrika 17, 195–208 (1952)CrossRefMATHGoogle Scholar
  29. 29.
    I.C. Ross, F. Harary, Identification of the liaison persons of an organization using the structure matrix. Manag. Sci. 1, 251–258 (1955)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    I.C. Ross, F. Harary, A description of strengthening and weakening members of a group. Sociometry 22, 139–147 (1959)MathSciNetCrossRefGoogle Scholar
  31. 31.
    M.S. Sunitha, A. Vijayakumar, Blocks in fuzzy graphs. J. Fuzzy Math. 13(1) 13–23 (2005)Google Scholar
  32. 32.
    M.S. Sunitha, A. Vijayakumar, A characterization of fuzzy trees. Inf. Sci. 113, 293–300 (1999)MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    E. Takeda, T. Nishida, An application of fuzzy graph to the problem concerning group structure. J. Oper. Res. Soc. Jpn. 10, 217–227 (1976)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMATHGoogle Scholar
  35. 35.
    L.A. Zadeh, Similarity relations and fuzzy orderings. Inf. Sci. 3, 177–200 (1971)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • John N. Mordeson
    • 1
  • Sunil Mathew
    • 2
  • Davender S. Malik
    • 1
  1. 1.Department of MathematicsCreighton UniversityOmahaUSA
  2. 2.Department of MathematicsNational Institute of TechnologyCalicutIndia

Personalised recommendations