On Deterministic Soft Sets: Algebraic Properties and Their Application to Electoral Decision Making

Abstract

Deterministic Soft Set (DSS) Theory extends classical soft set theory by 
incorporating deterministic external factors into parameterized representations of 
uncertainty. However, several fundamental structural properties required for a 
comprehensive mathematical framework remain undeveloped. This study strengthens 
the theoretical foundation of DSS Theory by formulating and establishing key 
algebraic and relational properties of deterministic soft sets. A reduction criterion 
is derived to characterize the conditions under which a deterministic soft set 
reduces to a classical soft set, thereby clarifying the relationship between the two 
frameworks. Formal definitions and associated properties are developed for 
deterministic equality and inclusion, null and absolute deterministic soft sets, and 
the deterministic NOT operation. The study further introduces deterministic soft 
equivalence relations and deterministic soft partitions and establishes their 
fundamental mathematical characteristics. It is demonstrated that deterministic 
soft inclusion satisfies reflexivity, antisymmetry, and transitivity and therefore 
defines a partial order on the collection of deterministic soft sets. Furthermore, a 
correspondence between deterministic soft equivalence relations and deterministic 
soft partitions is established, providing an important structural link within the DSS 
framework. The practical applicability of the extended theory is demonstrated using 
an electoral candidate-selection problem in which alternatives are evaluated with 
respect to specified parameters and deterministic external factors. A deterministic 
support-based decision model is applied to aggregate the resulting evaluations, 
identifying candidate c₂ as the preferred alternative under the prescribed 
conditions. The findings provide a more rigorous structural foundation for DSS 
Theory and broaden its applicability to parameter-dependent decision-making 
problems involving explicitly defined deterministic contextual factors.