On soft quantum B-algebras and fuzzy soft quantum B-algebras (Q2051626)

Summary: This paper aims to make a combination between the quantum B-algebras (briefly, \(\mathscr{X}\)-\(\mathbb{A}\)s) 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, \(\mathbb{SQB}\)-\(\mathbb{A}\)s), a soft deductive system of \(\mathbb{QB}\)-\(\mathbb{A}\)s, and deducible soft quantum B-algebras (briefly, \(\mathbb{DSQB}\)-\(\mathbb{A}\)s). Then, we discuss the relationship between \(\mathbb{SQB}\)-\(\mathbb{A}\)s and \(\mathbb{DSQB}\)-\(\mathbb{A}\)s. Furthermore, we investigate the union and intersection operations of \(\mathbb{DSQB}\)-\(\mathbb{A}\)s. Secondly, we introduce the notions of a fuzzy soft quantum B-algebras (briefly, \(\mathbb{FSQB}\)-\(\mathbb{A}\)s), a fuzzy soft deductive system of \(\mathbb{QB}\)-\(\mathbb{A}\)s, and present some characterizations of \(\mathbb{FSQB}\)-\(\mathbb{A}\)s, along with several examples. Finally, we explain the basic properties of homomorphism image of \(\mathbb{FSQB}\)-\(\mathbb{A}\)s.