Fuzzy linear programming problem 1, general approach and flexible linear programming problem

Linear programming is one of the most practical decision-making models in real world problems. Sometimes the values of the coefficients of the decision-making problem are not clearly clear and may include ambiguities. This is where the use of fuzzy set theory is highly regarded by researchers. Fuzzy linear programming is a model of optimization problem in which the objective function and constraints of linear functions include ambiguous parameters and these ambiguities are modeled with fuzzy concepts. In fuzzy linear programming problems and in terms of the position of the ambiguities in the problem, different states are created that different solutions are presented for each of these states. In this research, the introduction of fuzzy linear programming, types of ambiguities in the problem in fuzzy environment and different categories of fuzzy linear programming problems based on the type of ambiguity in these types of problems and generally the problems of flexible fuzzy linear programming are investigated. Ambiguities in these types of issues are vagueness type and are expressed by membership functions. In these types of ambiguity problems in the target function, fuzzy cost coefficients, fuzzy constraint matrix and fuzzy resource vector or combining these states together, each of these ambiguities creates different states that are expressed and the existing solving methods for each state are examined and several numerical examples are given for better understanding.