An innovative fuzzy Revan index with CRITIC integration in multi-criterion decision-making.

This study introduces the fuzzy Revan index (FRI), a new comprehensive index of fuzzy graphs that can be used to facilitate multi-criteria decision-making under uncertainty. Unlike other fuzzy graph indices that only consider local structural properties, the FRI uses membership values for both vertices and edges to identify larger connectivity patterns. We defined its theoretical properties, such as the upper bounds of particular classes of graphs, and implemented a computational algorithm with a pseudocode that can be used for large-scale networks. In this context, the FRI was integrated with a CRITIC-based approach to make decisions, wherein the membership values were calculated using the sigmoid and multiplicative methods. A national highway site selection problem was considered to illustrate the relevance of the proposed approach for real-world applications. Six site locations were evaluated based on a fuzzy graph derived from five weighted criteria: land acquisition price, environmental considerations, geotechnical suitability, accessibility, and future expansion potential. Combining FRI values with a multi-criteria decision-making method provides a more comprehensive site ranking than that obtained using local measurements. The findings indicate how FRI can enhance the quality of evaluation in uncertain and complex settings and its wider application in the field of information science.