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

This paper investigates engineering decision optimization in uncertain environments. Subject to constraints on cost and expected returns, engineering decisions optimize material input, equipment selection and process arrangement to minimize costs and maximize economic benefits. As an efficient formal verification technique, model checking offers a new approach to addressing this problem. Traditional model checking focuses on qualitative verification, while quantitative approaches, including probabilistic and possibilistic model checking, have been gradually developed. Among them, possibilistic model checking is more applicable to systems with fuzzy uncertainty. However, existing possibilistic model-checking techniques have notable limitations: they are only designed for closed systems and ignore interactions between the system and external environments; their simplistic information aggregation leads to information asynchrony and loss; and they cannot model and verify systems with incomplete information. Model checking based on possibilistic decision processes enables the selection of uncertain actions and initially resolves the modeling and verification of open systems. In our previous work, we introduced quality constraints into possibilistic temporal logic to mitigate information asynchrony and loss. We also established the theories of intuitionistic fuzzy Kripke structure (IFKS) and Intuitionistic Fuzzy Computation Tree Logic (IFCTL), which support the modeling and verification of systems with incomplete information. To improve the practicality and accuracy of engineering decisions, this study adopts the ideas of uncertain decision-making behavior selection, quality constraints and incomplete information modeling. It extends IFKS to the Weighted Intuitionistic Fuzzy Kripke Structure (WIFKS) and evolves IFCTL into the intuitionistic fuzzy decision tree logic (IFDTL). We further propose an IFDTL model-checking algorithm and a multi-attribute engineering decision algorithm based on the proposed method, along with corresponding correctness proofs and complexity analysis. A case study on Qinling health-preserving tourism planning verifies the rationality and effectiveness of the presented approach. This research provides a novel formal solution for engineering decision-making under uncertainty.