The minimum weight dominating set problem (MWDSP) has been a popular research topic in recent years. The weights of vertexes may be considered as cost, time, or opponent’s payoff, which are uncertain in most cases. This paper discusses MWDSP under hybrid uncertain environments where the weights of vertexes are random fuzzy variables. First, random fuzzy theory is introduced to describe these hybrid uncertain variables. Then we propose three decision models based on three different decision criteria to solve MWDSP under hybrid uncertain environments. To solve the proposed models, we present a hybrid intelligent algorithm where random fuzzy simulation and genetic algorithm are embedded. Numerical experiments are performed in the last to show the robustness and effectiveness of the presented hybrid intelligent algorithm.

Edge covering problem, dominating set problem, and independent set problem are classic problems in graph theory except for vertex covering problem. In this paper, we study the maximum independent set problem under fuzzy uncertainty environments, which aims to search for the independent set with maximum value in a graph. First, credibility theory is introduced to describe the fuzzy variable. Three decision models are performed based on the credibility theory. A hybrid intelligence algorithm which integrates genetic algorithm and fuzzy simulation is proposed due to the unavailability of traditional algorithm. Finally, numerical experiments are performed to prove the efficiency of the fuzzy decision modes and the hybrid intelligence algorithm.

Edge covering problem, dominating set problem, and independent set problem are classic problems in graph theory except for vertex covering problem. In this paper, we study the maximum independent set problem under fuzzy uncertainty environments, which aims to search for the independent set with maximum value in a graph. First, credibility theory is introduced to describe the fuzzy variable. Three decision models are performed based on the credibility theory. A hybrid intelligence algorithm which integrates genetic algorithm and fuzzy simulation is proposed due to the unavailability of traditional algorithm. Finally, numerical experiments are performed to prove the efficiency of the fuzzy decision modes and the hybrid intelligence algorithm.