In this paper, decomposition theorems of picture fuzzy set (PFS) have been proved. (⍺,δ,β)-cut of picture fuzzy set have been defined and some of its properties are studied. Later on extension principle for PFS has been defined and studied some of its properties. Finally, picture fuzzy arithmetic based on extension principle has been performed.
Fuzzy set, Fuzzy arithmetic, Extension principle, Picture fuzzy set
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