Abstract
This paper aims to make a combination between the quantum B-algebras (briefly, X-As) and two interesting theories (e.g., soft set theory and fuzzy soft set theory). Firstly, we propose the novel notions of soft quantum B-algebras (briefly, SDOUBLE-STRUCK CAPITAL QB-As), a soft deductive system of DOUBLE-STRUCK CAPITAL QB-As, and deducible soft quantum B-algebras (briefly, DSDOUBLE-STRUCK CAPITAL QB-As). Then, we discuss the relationship between SDOUBLE-STRUCK CAPITAL QB-As and DSDOUBLE-STRUCK CAPITAL QB-As. Furthermore, we investigate the union and intersection operations of DSDOUBLE-STRUCK CAPITAL QB-As. Secondly, we introduce the notions of a fuzzy soft quantum B-algebras (briefly, FSDOUBLE-STRUCK CAPITAL QB-As), a fuzzy soft deductive system of DOUBLE-STRUCK CAPITAL QB-As, and present some characterizations of FSDOUBLE-STRUCK CAPITAL QB-As, along with several examples. Finally, we explain the basic properties of homomorphism image of FSDOUBLE-STRUCK CAPITAL QB-As.