A thorough analysis of soft products from certain types of subsethood perspective: Part 2

Soft set theory has developed into a crucial mathematical paradigm for the formal representation and management of uncertaintysince Molodtsov's groundbreaking 1999 introduction. It provides a versatile and conceptually sound substitute for traditionalmethods. Its abstract generality and methodological adaptability have encouraged a growing corpus of theoretical research and realworld application in a variety of scientific fields. Soft set theory's operations are essential to its structural framework since they formthe algebraic foundation of the theory and have thus continued to be a subject of intense academic interest. Several soft productversions of the soft sets have been introduced within this operational landscape; nevertheless, the existing literature only offerspartial analyses of their relationships with respect to soft subsets. By providing a thorough and rigorous examination of this problem,the current study aims to address this shortcoming. It specifically addresses the essential circumstances under which one soft product,starting with symmetric difference and symmetric difference complement, is a soft subset of another soft product and when these softproducts are equal. In other words, the study has been extended to offer a more thorough examination of which soft product is asubset of another and the conditions that render them equal. In order to achieve this goal, the study clarifies a number of distributiveand structural characteristics that support the algebraic coherence of the soft product variations of the soft sets and demonstrate theircapacity to produce complex algebraic configurations. Therefore, the current theoretical exposition adds to a better understanding ofthe operational architecture of soft set theory and advances its fundamental algebraic framework. Beyond its inherent theoreticalvalue, this expanded analysis has significant theoretical importance because it clarifies the structural and hierarchical relationshipsbetween various soft products, improving algebraic comprehension of the internal structure of soft set theory and making it easier toidentify operational dependencies and equivalencies.