10.1007/s40096-021-00446-w

A new method for solving linear programming problems using Z-numbers’ ranking

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  • Fatemeh Hasankhani1,
  • Behrouz Daneshian2,
  • Tofigh Allahviranloo*3,
  • Farzin Modarres Khiyabani1,
  1. Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, IR
  2. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, IR
  3. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, TR Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IR

Published in Issue 2021-11-15

How to Cite

Hasankhani, F., Daneshian, B., Allahviranloo, T., & Khiyabani, F. M. (2021). A new method for solving linear programming problems using Z-numbers’ ranking. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00446-w
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Abstract

Abstract In this paper, the concept of the full Z-linear programming problem (FZLP) is first introduced. It is worth to mention that in these type of problems, all parameters, including the coefficients of variables in the objective functions, the coefficients of the variables in the constraints, the right-hand side of the constraints, as well as the decision variables, are valued as Z-numbers. Clearly, it is critical to provide a method to solve these types of problems, and to find their optimal solutions. Therefore, this paper develops a novel and practical method to find the solution of the problem using the concept of Z-numbers. To prove the applicability of the concept, two illustrative examples are provided to demonstrate the precision and effectiveness of this method.

Keywords

  • Z-Number,
  • Z-Linear Programming,
  • Triangular Fuzzy Number,
  • Z-Ranking

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