By generalizing the definition of fuzzy weakly semicontinuous mappings by B. S. Zhong, we introduce the concept of fuzzy weakly r-semicontinuous mappings in fuzzy topology of Chattopadhyay. Then the concept introduced by B. S. Zhong becomes a special case of our definition. Also, we show that fuzzy weakly r-semicontinuity and fuzzy weakly r-continuity are independent notions.