An interactive method for the solution of fully Z-number linear programming models

Linear programming is a technique widely used in decision-making nowadays. Linear programming in a fuzzy environment makes it even more interesting due to the vagueness and uncertainty of the available resources and variables. Since the market price and profit of certain goods are not known exactly, considering fuzzy variables and parameters in the linear programming makes it more closer to the real-life situation; therefore, it becomes more attractive for the decision-makers. In a fuzzy environment, there is only one information and that is the possibility of the variable. In many real-world problems, we need the reliability of the information along with its possibility. Zadeh suggested a Z-number Z = (A; B) with two components, A carrying the information of possibility of the variable, and B carrying the information about reliability of the first component A. Linear programming with its parameters and variables carrying the information in the form of Z number is even more exciting for the decision-makers. Because every decision-maker demands information that is more reliable, linear programming in a Z-number environment with both its components taken as fuzzy numbers is a very attractive problem. In this paper, we present linear programming problems with the parameters and variables taken as Z number having triangular fuzzy numbers as possibility and reliability. We also suggest an interactive method to solve Z number linear programming problems by converting Z-numbers into conventional fuzzy numbers and then using the ranking of fuzzy numbers. We also present applications of the proposed models by solving numerical examples. We also test the authenticity of the proposed method by comparing the results with the existing techniques.