An intuitionistic fuzzy soft set method for stochastic decision-making applying prospect theory and grey relational analysis

Intuitionistic fuzzy sets and soft sets describe the different types of uncertainty. Their fusion gets intuitionistic fuzzy soft sets, forms a more powerful mathematical tool for uncertainty description and further enlarges the scope of applications. This is more advantageous to solve decision-making problems. This paper proposes an intuitionistic fuzzy soft set method for stochastic decision-making applying prospect theory and grey relational analysis. According to the known evaluation information, this method describes stochastic decision-making problems as intuitionistic fuzzy soft sets. Firstly, a score function is defined and intuitionistic fuzzy numbers are converted the values of this score function. Secondly, the prospect decision matrix is given by utilizing the prospect value formula. Thirdly, the weight of each parameter is determined through grey relational analysis. Fourthly, the comprehensive prospect value of each scheme is gotten on the basis of the weight of each parameter. Fifthly, the optimal choice is obtained according to the comprehensive prospect values. Sixthly, an algorithm is presented. Finally, two applied examples are employed to illustrate the effectiveness and feasibility of this method.