Abstract
The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of (M,N)-SI-hemirings ((M,N)-SI-h-ideals) of hemirings, which are generalizations of SI-hemirings (SI-h-ideals). By soft union-intersection sums (products), some related properties are discussed. Special attention is paid to quotient soft hemirings. Finally, we investigate some characterizations of h-hemiregular hemirings by means of (M,N)-SI-h-ideals.