Intuitionistic Fuzzy Decision Trees Temporal Logic and Its Application in Engineering Decision-Making

This paper focuses on the optimization of engineering decision-making under uncertain environments. Engineering decision-making requires optimizing the input of production materials and the selection of equipment and processes under the constraints of cost and expected return to minimize costs and maximize production benefits. As an efficient formal verification technique, model checking provides a new approach to solve this problem. Traditional model checking mainly focuses on qualitative verification, while quantitative model checking techniques (such as probabilistic and possibilistic model checking) have been developed gradually, among which possibilistic model checking is more suitable for systems with fuzzy uncertainty. However, existing possibilistic model checking techniques have obvious defects: first, they only target closed systems and do not consider the interaction between the system and the external environment; second, the simple information aggregation method leads to information desynchronization and information loss; third, they cannot model and verify systems with incomplete information. Model checking technology based on possibilistic decision processes considers uncertain action selection and initially solves the problem of modeling and verification of open systems. The author has introduced the idea of quality constraints into possibilistic temporal logic to solve the problems of information desynchronization and information loss in possibilistic model checking; moreover, the author has established the theories of Intuitionistic Fuzzy Kripke Structure (IFKS) and Intuitionistic Fuzzy Computation Tree Logic (IFCTL), which can model and verify systems with incomplete information. To improve the usability and accuracy of engineering decisions, this paper will draw on the ideas and methods of uncertain selection of decision behaviors, quality constraints, and incompleteness modeling, extend IFKS to Weighted Intuitionistic Fuzzy Kripke Structure (WIFKS), induce IFCTL to Intuitionistic Fuzzy Decision Tree Logic (IFDTL), propose an algorithm for solving IFDTL model checking problems, and present a solution algorithm for multi-attribute engineering decision-making based on IFDTL model checking, along with its correctness proof and complexity analysis. Finally, a case study of Qinling health-preserving tourism planning is given to verify the rationality and efficiency of the proposed method, providing a new formal solution for uncertain engineering decision-making.