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In this paper, some properties of a BPFR were studied. Also, level sets of BPFRs were studied with their properties. Some results were given and, in some cases, examples and counter-examples were constructed. In particular, we have shown that if a BPFR Q is a subset of another BPFR ρ, (s, t)-level (or strong level) subsets of Q are classical subsets of the (s, t)-level (or strong level) subsets of ρ and that the strong level subsets of a BPFR is a subset of the ordinary level subset of the same among others. By these, we have improved on some of the results in the previous work and have laid the right foundation for further works on these concepts.