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, $\mathcal{X}$ - $\mathbb{A}$ 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, $\mathbb{S}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s), a soft deductive system of $\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s, and deducible soft quantum B-algebras (briefly, $\mathbb{DS}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s). Then, we discuss the relationship between $\mathbb{S}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s and $\mathbb{DS}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s. Furthermore, we investigate the union and intersection operations of $\mathbb{DS}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s. Secondly, we introduce the notions of a fuzzy soft quantum B-algebras (briefly, $\mathbb{FS}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s), a fuzzy soft deductive system of $\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s, and present some characterizations of $\mathbb{FS}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s, along with several examples. Finally, we explain the basic properties of homomorphism image of $\mathbb{FS}\mathbb{Q}\mathbb{B}$ - $\mathbb{A}$ s.