On Optimizing Neutrosophic Complex Programming Using Lexicographic Order


  • Hamiden Abd El-Wahed Khalifa Cairo University, Giza, Egypt
  • Pavan Kumar Koneru Lakshmaiah EducationFoundation, Vaddeswaram, AP, INDIA-522502
  • Florentin Smarandache University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA


Complex programming;, Neutrosophic numbers, Score function, Lexicographic order, Lingo software, Kuhn-Tucker conditions, Neutrosophic optimal solution


Neutrosophic sets are considered as a generalization of the crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. This paper aims to characterize the solution of complex programming (CP)problem with imprecise data instead of its prices information. The neutrosophiccomplex programming (NCP)problem is considered by incorporating single valued trapezoidal neutrosophic numbers in all the parameters of objective function and constraints. The score function corresponding to the neutrosophic number is used to transform the problem into the corresponding crisp CP. Here, lexicographic order is applied for the comparison between any two complex numbers. The comparison is developed between the real and imaginary parts separately. Through this manner, the CP problem is divided into two real sub-problems.In the last, a numerical example is solved for the illustration that shows the applicability of the proposed approach.The advantage of this approach is more flexible and makes a real-world situation more realistic.


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How to Cite

El-Wahed Khalifa, H. A., Kumar, P. ., & Smarandache, F. . (2020). On Optimizing Neutrosophic Complex Programming Using Lexicographic Order. Neutrosophic Sets and Systems, 32, 330-343. Retrieved from http://fs.unm.edu/NSS2/index.php/111/article/view/383