Search Results (4)

In the context of multi-autonomous underwater vehicle (multi-AUV) operations, the target assignment is addressed as a multi-objective allocation (MOA) problem. The selection of strategy for multi-AUV target allocation is dependent on the current non-cooperative environment. This paper establishes a multi-AUV allocation situation advantage evaluation system to assess and quantify the non-cooperative environment. Based on this framework, a multi-AUV target allocation model using a bi-matrix game theory is developed, where multi-AUV target allocation strategies are considered as part of the strategic framework within the game. The payoff matrix is constructed based on factors including the situational context of multi-AUV operations, effectiveness, and AUV operational integrity. The Nash equilibrium derived from the game analysis serves as the optimal solution for resource distribution in multi-AUV non-cooperative scenarios. To address the challenge of finding the Nash equilibrium in bi-matrix games, this paper introduces a repulsion process quantum particle swarm optimization (RPQPSO) algorithm. This method not only resolves the complexities of Nash equilibrium computation but also overcomes the limitations of traditional optimization methods that often converge to local optima. A simulation experiment of multi-AUV operations is designed to validate the multi-AUV target allocation model, demonstrating that the RPQPSO algorithm performs effectively and is applicable to multi-AUV task scenarios. Full article

Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has at least one Pareto–Nash equilibrium. Then, with the help of BGIP, we obtain the necessary and sufficient conditions for the existence of fuzzy Pareto–Nash equilibrium of MBGFP. Secondly, based on the bilinear programming method for calculating Nash equilibrium in crisp bi-matrix games, we established a bilinear programming method with parameters for calculating fuzzy Pareto–Nash equilibrium. By considering the importance of each objective to the players, MBGFP is transformed into a bi-matrix game with fuzzy payoffs (BGFP). Furthermore, we obtained the necessary and sufficient conditions for the existence of fuzzy weighted Pareto–Nash equilibrium and its calculation method. Finally, a practical example is used to illustrate the effectiveness of our proposed calculation method. Full article

Uncertainty is common in miscellaneous decision-making problems, including bi-matrix games. The uncertainty of bi-matrix games is caused by the complexity of the game environment and the limitations of players’ cognition rather than the asymmetry of information. Therefore, it is hard for players to precisely give their crisp payoff values. In this paper, a new method considering the acceptance degree that the general intuitionistic fuzzy constraints may be violated is developed to solve general intuitionistic fuzzy bi-matrix games (GIFBMGs). In the method, a new asymmetric general intuitionistic fuzzy number (GIFN) and its cut sets are firstly defined. Then, the order relationship of GIFNs and the definitions of α and β-bi-matrix games are proposed. Afterwards, the constructed general intuitionistic fuzzy quadratic program is converted into an interval bi-objective program on the basis of the order relationship of GIFNs. Furthermore, the interval bi-objective program is converted into a multi-objective quadratic program based on the combination of interval order relationship and the player’s acceptance degree. A goal programming approach is put forward to solve the multi-objective quadratic program. Finally, the validity of the proposed method is verified with a numerical example for corporate environmental behavior (CEB), and some comparative analyses are conducted to show the superiority of the proposed method. Full article

A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are demonstrated through a numerical example. Full article