A Study on Continuous Linear Knapsack Problems with Fuzzy Random Variable Coefficients

Abstract

In this paper, we consider a continuous type knapsack problem involving fuzzy random variable coefficients. First, we formulate the problem to maximize a degree of possibility that the objective function value satisfies a fuzzy goal. Since the degree of possibility varies randomly, we consider the model based on the fractile optimization model in stochastic programming. After transforming the problem into the deterministic equivalent problem, we propose a polynomial order algorithm for solving the problem efficiently and obtain the time complexity.