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