On Soft Quantum B-Algebras and Fuzzy Soft Quantum B-Algebras

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, SℚB-As), a soft deductive system of ℚB-As, and deducible soft quantum B-algebras (briefly, DSℚB-As). Then, we discuss the relationship between SℚB-As and DSℚB-As. Furthermore, we investigate the union and intersection operations of DSℚB-As. Secondly, we introduce the notions of a fuzzy soft quantum B-algebras (briefly, FSℚB-As), a fuzzy soft deductive system of ℚB-As, and present some characterizations of FSℚB-As, along with several examples. Finally, we explain the basic properties of homomorphism image of FSℚB-As.