Triangular Norm-Based Interval Valued L-Fuzzy Soft Ideals in Nearrings

Jagadeesha B; Sabina Rachana Crasta

doi:10.5269/bspm.80120

Jagadeesha B St Joseph Engineering College, Vamanjoor Mangaluru
Sabina Rachana Crasta St Joseph Engineering College, Vamanjoor, Mangaluru, Karnataka India 575028

Resumen

This study explores interval-valued L-fuzzy soft ideals within nearrings, where this structure
is established over a complete bounded lattice. The approach employs interval-valued triangular norms and conorms as tools for handling graded membership and uncertainty. The algebraic characteristics of these ideals are examined, together with their behavior under nearring homomorphisms and the corresponding coset structures. We also analyze the relationship between such ideals and their associated level sets, thereby extending the scope of fuzzy soft algebraic theory. The framework not only brings together earlier notions of fuzzy and soft ideals but also introduces threshold-based flexibility, which broadens its range of applicability. Possible applications include decision-making, reasoning under uncertainty, and computational intelligence,
particularly in contexts where algebraic precision and soft set-based modeling need to be combined.

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