Maji et al. introduced the concept of a fuzzy soft set, which is an extension to the concept of a soft set. In this paper, we apply the concept of a fuzzy soft set to hemiring theory. The concepts of \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft left h-ideals (right h-ideals, h-bi-ideals, and h-quasi-ideals) are introduced, and some related properties are obtained. The notion of left (right) h-hemiregular hemirings is provided. Some characterization theorems of (left) h-hemiregular and (left) duo hemirings are derived in terms of \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft left (right) h-ideals, \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft h-bi-ideals, and \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft h-quasi-ideals.