Cubic Soft Ideals on B-algebra for Solving Complex Problems: Trend Analysis, Proofs, Improvements, and Applications

Abstract

In this paper, we introduce the concepts of cubic soft (CS) algebra, CS o-subalgebra, and CS ideals within the framework of B-algebra. We provide comprehensive characterizations of these new structures, elucidating their unique properties and interrelationships. Specifically, we present detailed conditions under which a CS subalgebra can be classified as a closed CS ideal. Our analysis explores the intricate relationships among closed cubic soft ideals, cubic soft subalgebras, and cubic soft o-subalgebras. By doing so, we aim to provide a deeper understanding of how these structures interact and coexist within the broader context of B-algebra The findings offer significant insights into the application and theoretical underpinnings of cubic soft sets in algebraic systems, contributing to the ongoing evolution of fuzzy set theory and its applications in various mathematical domains. Our work not only broadens the scope of B-algebra but also enhances its utility in solving complex problems where traditional algebraic approaches may fall short. Through this exploration, we seek to advance the field and open new avenues for research and practical applications in mathematical sciences.