Yildiz, SevdaBayram, Nilay Sahin2026-04-252026-04-2520250354-5180https://doi.org/10.2298/FIL2532621Yhttps://hdl.handle.net/11486/8549In this study, we introduce and investigate new forms of convergence, namely, P-statistical relative pointwise, uniform, and P-equi-statistical relative convergence, for sequences of functions whose values lie in the space of fuzzy numbers. These notions, motivated by a synthesis of statistical and relative convergence frameworks, are explored both in terms of their structural characteristics and mutual interrelationships. Furthermore, we examine the behavior of their corresponding r-level sets to provide deeper insight into their convergence dynamics. As a principal application, we apply approximation theorems of Korovkin-type for sequences of functions with fuzzy values under the newly proposed modes of convergence, and we compute the rate of convergence.eninfo:eu-repo/semantics/closedAccessFuzzy-number-valued functionP-equi-statistical relative convergencefuzzy Korovkin theoryArticle3932116211163610.2298/FIL2532621Y2-s2.0-105025685352Q2WOS:001640714600001Q2