Algorithm for solving optimization problems using Interval Valued Probability Measure

We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval valued probability measure (IVPM), we present IVPM´s interval expected values whose possibility density functions are in the form of polynomials. By working with the endpoints of interval expected values of independent uncertain coefficients in a linear optimization problem, we turn the uncertain problem to four deterministic ones. These problems lead us to the bounds of our solution and objective value and we use the midpoint of these bounds to represent the problem. Moreover, linear optimization problems containing all three types of uncertainties can be solved using this framework.