Objectives: This study aimed to validate the application of the 3 × 2 achievement goal model in sports. Motivations: In order to offer new perspectives on achievement goals, this study explores 3 × 2 achievement goals used in competitive sports, and the prediction of passion and psychological well-being for sports. Methods: The study sample consists of 406 college and university athletes, including 230 males and 176 females. Average age of the subjects was 20.34 years. Average length of years of sports participation was 8.23 years. Data were collected with a questionnaire that incorporated a 3 × 2 achievement goal scale, a sports passion scale, and the Psychological Well-Being Scale. Statistical Methods: Data were analyzed using descriptive statistics for fuzzy data, fuzzy correlation coefficients, and fuzzy regression models. Finding: 1. There was a correlation between every two of task-approach, task-avoidance, self-approach, self-avoidance, other-approach, other-avoidance, harmonious passion, obsessive passion, and psychological well-being. 2. Among college and university athletes, task-approach and self-approach positively influence harmonious passion; task-approach, self-approach, other-approach, and other-avoidance positively influence obsessive passion; task-avoidance negatively influences obsessive passion; task-approach and self-approach positively influence psychological well-being, and task-avoidance negatively influences psychological well-being. Innovations: Use of the 3 × 2 achievement goal scale is applicable to college sportsmen in Taiwan, and the research method uses fuzzy statistical analysis, which breaks through the barriers of traditional psychological survey methods, and will improve the research quality of the sample survey. This study provides new techniques for research on psychological trends in sports. Value: In the future, coaches and athletes should focus on task-approach and self-approach goals in order to enhance the college or university athletes’ harmonious passion for a positive impact on their psychological well-being when they engage in sports through their own free will.

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