Knapsack problem in fuzzy nature: Different models based on credibility ranking method

This paper deals with knapsack problem in fuzzy nature, where both the objective function and constraints are considered to be fuzzy. Three different models for fuzzy knapsack problem are proposed including, expected value model, chance-constrained model, and dependent-chance model. Credibility ranking method is applied to convert the fuzzy models into a crisp equivalent linear one considering triangular and trapezoidal fuzzy numbers. The solution of the fuzzy problem is obtained with respect to different satisfaction degrees in the objective function and constraints. Several numerical examples are given to demonstrate different models and concepts. The proposed approaches are applied to model and to solve a fuzzy pre-disaster investment decision problem.