Full Fuzzy-Parameterized Fuzzy Soft Set: Theory and Applications
DOI:
https://doi.org/10.65405/t2n4wr78Keywords:
fuzzy set, soft set, parameterized fuzzy soft set, full fuzzy soft set, uncertainty modelingAbstract
In this paper, we introduce a new mathematical structure called the Full Fuzzy-Parameterized Fuzzy Soft Set (FFPFSS), which extends both fuzzy soft sets and fuzzy-parameterized soft sets by incorporating dual fuzziness: fuzziness in parameters and fuzziness in the underlying soft set mapping. We provide a formal definition of the FFPFSS along with its fundamental properties, algebraic operations, and structural characteristics. Several theorems and propositions are established to demonstrate its behavior under union, intersection, complement, and inclusion relations. Furthermore, a decision-making model based on the proposed framework is developed and applied to real-world scenarios. Comparative analysis shows that the FFPFSS generalizes existing models and offers greater flexibility in handling uncertainty, parameter variability, and imprecise information.
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