A method to find the unique optimal fuzzy value of fully fuzzy linear programming problems with inequality constraints having unrestricted L-R fuzzy parameters and decision variables

An epsilon‐constraint method for fully fuzzy multiobjective linear programming

“…This section presents some basic definitions from fuzzy sets theory concerning LR fuzzy numbers, and a brief discussion on lexicographic criteria for ranking LR fuzzy numbers. For the sake of completeness, we also include a detailed exposition of the method proposed in Reference for finding unique optimal fuzzy values of FFLP problems with equality and inequality constraints.…”

“…In this section, we present the method proposed in Reference for finding unique optimal fuzzy values of FFLP problems with equality and inequality constraints. We begin with the mathematical formulation of FFLP problems, basic definitions and remarks on some existing solution methodologies.…”

“…In this paper, we show that the use of a single linear ranking function for making crisp transformations does not guarantee Pareto optimal fuzzy solutions of fuzzy MOLP problems. We extend to FFMOLP recent results on the single-objective case obtained in Reference 15 and propose an epsilon-constraint method for FFMOLP that produces only Pareto optimal fuzzy solutions with respect to a lexicographic criterion for ranking LR fuzzy numbers. To this aim, Section 2 presents several basic definitions from fuzzy sets theory, remarks on lexicographic criteria for ranking LR fuzzy numbers and the method of Pérez-Cañedo and Concepción-Morales 15 for solving FFLP problems.…”

“…We extend to FFMOLP recent results on the single-objective case obtained in Reference 15 and propose an epsilon-constraint method for FFMOLP that produces only Pareto optimal fuzzy solutions with respect to a lexicographic criterion for ranking LR fuzzy numbers. To this aim, Section 2 presents several basic definitions from fuzzy sets theory, remarks on lexicographic criteria for ranking LR fuzzy numbers and the method of Pérez-Cañedo and Concepción-Morales 15 for solving FFLP problems. Some methodologies for handling inequality constraints in FFLP are briefly discussed in this section as well.…”

“…Pérez‐Cañedo and Concepción‐Morales proposed a lexicographic method to find unique optimal values of single‐objective fully fuzzy linear programming (FFLP) problems with equality and inequality constraints, in which the problem parameters and decision variables can take on unrestricted LR fuzzy numbers. In that work, the fuzzy inequality relations in the constraint set were defined by using lexicographic ranking criteria with the total order properties, such as those given in References …”