This study explores the concept of minimum connected domination in fuzzy graphs, focusing on defining and analyzing key parameters such as adjacent dominating sets and independent domination sets. Through the examination of fuzzy semi graphs, particularly in the context of end, strong, and consecutive domination, the research contributes to the theoretical understanding of domination theory within fuzzy frameworks. Despite its theoretical rigor, the study identifies limitations in practical applications and the absence of efficient algorithms for real-world implementation. Future research directions are proposed to investigate dynamic fuzzy semi graphs, develop computational methods, and apply these theoretical concepts to practical scenarios, thereby enhancing their relevance and utility in various fields.