Small and Medium Enterprises (SMEs) are vital for growth and employment in both developed and developing countries. This study investigates the problems faced by SMEs in Bhutan and their adoption of competitive growth strategies. This study used purposive sampling to survey 95 manufacturing SMEs from Phuntsholing and Thimphu in Bhutan. Descriptive statistics were derived using cross tabulation and frequency tables, while the Fuzzy Analytic Hierarchy Process (FAHP), a computational intelligence (CI) method, was used to prioritize the problems and strategies. This study demonstrates the application of CI in multi-criteria decision analysis (MCDA) in social sciences. Due to the small sample size, the Fisher Exact test was used for inference. The literature identifies various challenges for SMEs, including infrastructure (roads, power, water, sewage, telecommunication, security), access to finance, human resources, technology, industry-specific issues, and international market access. Encouragingly, this study found that 95% of respondents had access to roads and power, 92% to water supply and telecommunication, 84% to a functional sewage system, and 88% to good security. The competitive strategies adopted by SMEs include customer focus, new market development, new product development, market segmentation, reverse logistics, and product differentiation, with customer focus being the most prevalent strategy (90.5%).