Abstract
Picture fuzzy set (PFS) is a recent advancement tool to deal with vulnerability. It is an immediate expansion of intuitionistic fuzzy set that can display vulnerability in such circumstances including more responses of these kinds: indeed, decline, no. In this manuscript the idea of Picture fuzzy normed linear space (PFNLS) is discussed for the first time. Naturally PFNLS is an hybrid concept of PFS and normed linear space. Also Convergence in PFNLS are shown. Later on Completeness property on PFNLS are explored. Finally boundedness of Cauchy sequence in PFNLS is analysed.
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