Probability maximization model of 0–1 knapsack problem with random fuzzy variables

This paper considers a new model of 0-1 knapsack problem including probabilistic coefficients with ambiguous expected returns assumed as random fuzzy variables. Since the random fuzzy 0-1 knapsack problem is not well-defined integer programming problem due to involve random fuzzy variables, it is hard to construct the efficient solution method to solve this problem directly. In this paper, using chance constraints, possibility measure and fuzzy goal based on both stochastic and fuzzy programming approaches, the main problem is transformed into a deterministic equivalent quadratic integer programming. Then, the efficient solution method to find a strict optimal solution based on dynamic programming is constructed.