Measuring the research development, and innovation performance of Türki̇ye provinces using entropy and the grey relational method

In today's world, where knowledge- and technology-based economies are at the forefront, one of the most important factors determining a country's competitiveness is its R&D and innovation capacity. Accurately and objectively measuring this capacity not only at the national level but also at the regional and local level has become a critical requirement for increasing the effectiveness of development policies. Although Türkiye has experienced significant progress in R&D expenditures, a skilled workforce, patent production, and high-technology-focused production processes in recent years, there is a significant imbalance in the distribution of this progress across the provinces. This study evaluates the performance of Türkiye provinces within a multidimensional framework using 23 R&D and innovation indicators for 2024. First, the objective weights of each indicator were calculated using the Entropy method, and then the relative performance rankings of the provinces were determined using the Grey Relational Analysis (GRA) method. When the entropy weights obtained as a result of the analysis are examined, indicators such as Techno Investment (0.0744), Number of Design Centers (0.0742), and Number of Patent Registrations (0.0682) stand out as the criteria with the highest variance. According to the GIA results, Istanbul (0.97321), Ankara (0.53416), and Izmir (0.39188) ranked first three, respectively. The analysis results show that R&D and innovation activities in Türkiye are concentrated in specific regions and that regional development disparities also affect this area. The rankings and correlation degrees obtained as a result of the study will offer important implications for the design of regional innovation policies, more effective resource allocation, and reducing development disparities between provinces.