Applications and Computational Varieties of Free Soft Trioids
DOI:
https://doi.org/10.32350/sir.101.03Keywords:
computational applications, free soft trioid, soft set, soft trioidAbstract
Integrating soft set theory with multi-operational structures poses a foundational challenge In parameterized universal algebra,. In this paper, the theory of free soft trioids were developed establishing the existence and construction of free objects in the category SoftTrioid. Also we construct a non-restrictive definition of soft trioids equipped with pointwise operations with genuine context sensitivity. The free soft trioid being realized as a two-sorted term algebra prove the universal property and show that the word problem is decidable in linear time via a confluent rewriting system as the algorithmic implementations were supported by empirical validation. The relevance of our study were demonstrated by its applications in context-dependent type systems, formal verification, knowledge representation and access control thus situating soft trioid theory as a robust link between algebraic foundations and computational practice.
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