Posynomial Geometric Programming with Intuitionistic Fuzzy Coefficients

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


In this paper, we introduce posynomial geometric programming problems with intuitionistic fuzzy numbers, it is formulated in intuitionistic fuzzy environment introducing intuitionistic fuzzinees in objective and constraint coefficients. This paper presents an approach based on \((\alpha ,\beta )\)-cuts of intuitionistic fuzzy numbers to solve posynomial geometric programming problems with the data as triangular and trapezoidal intuitionistic fuzzy numbers.


Intuitionistic fuzzy set Triangular and trapezoidal intuitionistic fuzzy numbers Posynomial geometric programming \((\alpha , \beta )\)-cuts and interval-valued function 



Thanks to the support by National Natural Science Foundation of China (No. 70771030 and No. 70271047) and Project Science Foundation of Guangzhou University.


  1. 1.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer Physica Verlag, Heidelberg (1999)CrossRefMATHGoogle Scholar
  2. 2.
    Boyd, S., Kim, S.J., Vandenberghe, L., Hassibi, A.: Atutorial on Geometric Programming. Springer Science, Business Media, LLC (2007)Google Scholar
  3. 3.
    Creese, R.C.: Geometric programming for desing and cost optimization (with illustrative case study problems and solutions). Synthesis Lectures On Engineering (2010)Google Scholar
  4. 4.
    Dubey, D., Mehra, A.: Linear programming with triangular intuitionistic fuzzy number. In: EUSFLAT (2011)Google Scholar
  5. 5.
    Grzegorzewski, P.: Intuitionistic fuzzy numbers. In: Accepted for the Proceedings of the IFSA 2003 World CongressGoogle Scholar
  6. 6.
    Ishihashi, H., Tanaka, M.: Multiobjective programming in optimization of the interval objective function. Euro. J. Oper. Res. 48, 219–225 (1990)Google Scholar
  7. 7.
    Jianqiang, W., Zhong, Z.: Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. J. Syst. Eng. Electron. 20, 321326 (2009)Google Scholar
  8. 8.
    Li, D.F.: A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput. Math. Appl. 60, 1557–1570 (2010)Google Scholar
  9. 9.
    Li, D.F., Nan, J.X., Zhang, M.J.: A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. Int. J. Comput. Intell. Syst. 3, 522–530 (2010)Google Scholar
  10. 10.
    Mahapatra, G.S., Mandal, T.K.: Posynomial parametric geometric programming with interval valued coefficient. J. Optim. Theory Appl. 154, 120132 (2012)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Nachammai, A.L., Thangaraj, Dr. P.: Solving intuitionistic fuzzy linear programming by using metric distance ranking. Researcher 5(4), 65–70 (2013)Google Scholar
  12. 12.
    Rao, S.S.: Engineering Optimization Theory and Practice, 3rd edn. A Wiley Interscience Publication, Wiley, New York (1996)Google Scholar
  13. 13.
    Seikh, M.R., Nayak, P., Pal, M.: Generalized triangular fuzzy numbers in intuitionistic fuzzy environment. Int. J. Eng. Res. Dev. 5, 08–13 (2012)Google Scholar
  14. 14.
    Wang, J.Q., Zhang, Z.: Aggregation operators on intuitionistic fuzzy numbers and its applications to multi-criteria decision making problems. J. Syst. Eng. Electron. 20, 321–326 (2009)Google Scholar
  15. 15.
    Wei, G., Lin, R., Zhao, X., Wang, H.: Some aggregating operators based on the Choquet integral with fuzzy number intuitionistic fuzzy information and their applications to multiple attribute decision making. Control Cybern. 41 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education InstitutesGuangzhou UniversityGuangzhouChina
  2. 2.Guangzhou UniversityGuangzhouChina

Personalised recommendations