Optimization of Linear Objective Function Under \(\min -\)Probabilistic Sum Fuzzy Linear Equations Constraint

  • Ketty PeevaEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 657)


We present here linear optimization problem resolution, when the cost function is subject to fuzzy linear systems of equations as constraint.


  1. 1.
    Chen, L., Wang, P.: Fuzzy relational equations (I): the general and specialized solving algorithms. Soft Comput. 6, 428–435 (2002)CrossRefzbMATHGoogle Scholar
  2. 2.
    De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) Handbooks of Fuzzy Sets Series: Fundamentals of Fuzzy Sets, vol. 1, pp. 291–340. Kluwer Academic Publishers (2000)Google Scholar
  3. 3.
    Di Nola, A., Pedrycz, W., Sessa, S., Sanchez, E.: Fuzzy Relation Equations and Their Application to Knowledge Engineering. Kluwer Academic Press, Dordrecht (1989)CrossRefzbMATHGoogle Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA (1979)zbMATHGoogle Scholar
  5. 5.
    Grätzer, G.: General Lattice Theory. Akademie-Verlag, Berlin (1978)CrossRefzbMATHGoogle Scholar
  6. 6.
    Guu, S.M., Wu, Y.-K.: Minimizing a linear objective function with fuzzy relation equation constraints. Fuzzy Optim. Decis. Making 4(1), 347–360 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Klir, G.J., Clair, U.H.S., Yuan, B.: Fuzzy Set Theory Foundations and Applications. Prentice Hall PRT (1977)Google Scholar
  8. 8.
    Loetamonphong, J., Fang, S.-C.: An efficient solution procedure for fuzzy relational equations with max-product composition. IEEE Trans. Fuzzy Syst. 7(4), 441–445 (1999)CrossRefGoogle Scholar
  9. 9.
    MacLane, S., Birkhoff, G.: Algebra. Macmillan, New York (1979)zbMATHGoogle Scholar
  10. 10.
    Peeva, K.: Resolution of Fuzzy relational equations—method, algorithm and software with applications, information sciences. Special Issue (2011). doi: 10.1016/j.ins.2011.04.011
  11. 11.
    Peeva, K.: Inverse Problem Resolution for min-probabilistic sum Fuzzy relational equations—method and algorithm. In: 2012 VIth International IEEE Conference “Intelligent Systems”, vol. 1, pp. 489– 494. Sofia 6–8 Sept. (2012). ISBN 978-1-4673-2277-5Google Scholar
  12. 12.
    Peeva, K., Kyosev, Y.: Fuzzy relational calculus-theory, applications and software (with CD-ROM). In the Series Advances in Fuzzy Systems—Applications and Theory, vol. 22. World Scientific Publishing Company (2004)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Faculty of Applied Mathematics and InformaticsTechnical University of SofiaSofiaBulgaria

Personalised recommendations