A Constructive Proof of Fundamental Theory for Fuzzy Variable Linear Programming Problems
Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example.
A Constructive Proof of Fundamental Theory for Fuzzy Variable Linear Programming Problems,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 7,
2, Article 15.
Available at: https://digitalcommons.pvamu.edu/aam/vol7/iss2/15