Efficient strict solution methods for 0-1 random fuzzy programming problems based on the necessity measure

This paper considers two general 0-1 random fuzzy programming problems based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problems are not well defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goal for the objective function, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, each main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.