A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions

FFLP problem with symmetric trapezoidal fuzzy numbers

“…Since, in standard fuzzy arithmetic operations we have some problems in division and subtraction operations so there is no other option to solve fully fuzzy linear programming problems without converting them into the corresponding deterministic linear programs. In this paper a new method by using Ezzati et al (2014)'s fuzzy arithmetic operation and a fuzzy version of simplex algorithm is proposed for solving fuzzy linear programming problem whose parameters all are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method the fuzzy optimal solution of fully fuzzy linear programming problem can be easily obtained.…”

“…In this section, some basic definitions and arithmetic operations of symmetric trapezoidal fuzzy numbers are reviewed (Ezzati et al, 2014). In addition, a brief review of using ranking function and FFLP problem is given (Ganesan & Veeramani, 2006).…”

“…Recently, Ezzati et al (2014) defined a new operation on symmetric trapezoidal fuzzy numbers that the properties 1 and 0 are satisfied and based on new fuzzy arithmetic operations proposed, a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem was proposed, but their model was not fully fuzzy optimization. In this paper, a new method by using Ezzati et al (2014)'s fuzzy arithmetic operation and a fuzzy version of simplex algorithm is proposed for solving FFLP problem whose parameters all are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method the fuzzy optimal solution of FFLP problem can be easily obtained.…”

“…Others showed that the fuzzy arithmetic operation used by Khan et al (2013) had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al (2014) [Ezzati, R., Khorram, E., & Enayati, R. (2014). A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions.…”

Signed distance ranking based approach for solving bounded interval‐valued fuzzy numbers linear programming problems

“…The work by Kumar and Kaur proposed a new method to find the fuzzy optimal solution of FFLP problems with mixed constraints using ranking functions. The fuzzy primal and dual simplex algorithms were used for doing sensitivity analysis in FLP problems in the study by Ebrahimnejad and Verdegay, Based on two new fuzzy arithmetic operations and fuzzy ordering on symmetric TrFNs, a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic MOLP problem and a properly fuzzy efficient solution of a fuzzy MOLP problem was proposed in the study by Ezzati et al A solution methodology for solving FFLP problems in which the decision makers can be supported by yielding fuzzy efficient solutions under different uncertainty levels and risk attitudes has given in the study by Baykasoğlu and Subulan…”