Multiple Attribute Decision Method Based on Neutrosophic Z-Number Frank Combined Compromise Solution Approach

Abstract

Uncertain multi-attribute decision-making (MADM) represents a fundamental area within decision science, with extensive applications across various fields. The neutrosophic Z-number (NZN) offers a powerful framework for modeling uncertain information, as it captures not only the imprecise, incomplete, and inconsistent preferences of decision-makers but also the associated reliability of those preferences. This study develops a novel MADM approach by integrating the Combined Compromise Solution (CoCoSo) method, Frank aggregation operators, and the Logarithmic Decomposition of Criteria Importance (LODECI) model within the NZN context. Firstly, operational rules for NZNs are defined based on Frank triangular norms. Subsequently, the neutrosophic Z-number Frank weighted averaging (NZNFWA) and neutrosophic Z-number Frank weighted geometric (NZNFWG) operators, along with their ordered variants, are proposed to enhance the flexibility and robustness of aggregating NZN evaluations. To objectively determine attribute weights, an extended LODECI model grounded in the NZN score function is introduced. The enhanced CoCoSo method is then applied, utilizing the proposed aggregation operators to derive the final ranking of alternatives. The applicability and effectiveness of the proposed framework are demonstrated through a case study assessing green logistics development levels. Furthermore, a parameter sensitivity analysis and a comparative analysis with existing NZN-based methods are conducted to validate its robustness and superiority. The results confirm that the proposed NZN-LODECI-CoCoSo approach exhibits strong stability and practicality, providing an effective solution for complex decision-making problems under uncertainty.