Algorithms and Software Packages for Solving Transportation Problems With Intuitionistic Fuzzy Numbers

Infrastructure networks are critical components of contemporary society, and numerous approaches have been suggested for the selection of strategies to protect these networks. However, for uncertain environments, research on attack and defense game models for infrastructure networks is limited. Therefore, after reviewing the existing approaches, a method based on interval-valued intuitionistic fuzzy set (IVIFS) theory is proposed for attack and defense games in critical infrastructure networks. First, we present the process of constructing the game model proposed in this paper, which mainly includes the formulation of the cost model, the strategies, and the method of generating IVIFS payoffs. Next, the Nash equilibria of the game are identified by a pair of nonlinear programming models based on IVIFS theory. Finally, experiments are conducted on a target scale-free network, and an investigation into the variation patterns of the Nash equilibria under different circumstances is also conducted. We provide explanations for these variation patterns by considering payoffs from the perspective of mathematical programming models. Furthermore, we find that compared to the existing attack and defense game model with crisp payoffs, the model proposed in this paper leads to superior Nash equilibria. Our work is a preliminary attempt to analyse attack and defense games for infrastructure networks based on IVIFS theory, providing a method for assessing payoffs in uncertain environments for the attacker and defender. This topic deserves further study.

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Theory and Applications of the Software-Based PSK Method for Solving Intuitionistic Fuzzy Solid Assignment Problems

Kumar

2024

Advances in Logistics, Operations, and Management Science

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The real-life optimization problem, namely, the intuitionistic fuzzy solid assignment problem (IFSAP), is solved using the PSK (P. Senthil Kumar) method here. The mathematical model of IFSAP and its classifications are presented. Some standard results are provided. To find the optimal assignment of IFSAPs, many supporting theorems and corollaries are proved with the PSK method. Numerical examples and graphical illustrations are provided to illustrate the proposed model and theorems and the effectiveness of the method. The programming packages, namely, Matlab and Lingo, are used with the PSK method to solve the IFSAPs and to find out the optimum assignment and objective value. Additionally, the fruitfulness of the proposed method is illustrated through 3 numerical examples, and the results are compared with other methods and different software. Finally, the limitations of the proposed method and recommendations for the scope of future work are presented. It is useful for researchers, the public, and especially, governments to govern operations because it deals with real-life problems.

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Algorithms and Software Packages for Solving Transportation Problems With Intuitionistic Fuzzy Numbers

Cited by 3 publications

References 84 publications

Multi-objective mixed mode sugarcane transportation model using fuzzy NSGA

Multi-objective mixed mode sugarcane transportation model using fuzzy NSGA

Modelling attack and defense games in infrastructure networks with interval-valued intuitionistic fuzzy set payoffs

Theory and Applications of the Software-Based PSK Method for Solving Intuitionistic Fuzzy Solid Assignment Problems

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