Application of Gray Programming in Consumer Satisfaction Evaluation of Commercial Fitness Clubs

For commercial fitness clubs, consumer satisfaction is a key factor influencing conversion rates, renewal rates, and overall profitability. It is characterized by volatility, necessitating continuous assessment. This study, based on the gray 0-1 programming model, proposed an evaluation method that can identify and rank the indicators of consumer satisfaction in commercial fitness clubs, aiming to enhance consumer satisfaction and improve operator profits. In this context, consumers are defined as individuals with both demand and purchasing power, intending to purchase services or have already consumed them. The results demonstrate that although this method involves complex steps and high survey costs, its compensation effects and dynamic control advantages make it rational in practical applications. This not only promotes the use of gray programming in the interdisciplinary field of sports but also provides valuable insights into the sustainable development of commercial fitness clubs.