<![CDATA[This paper investigates the fundamental algebraic laws and properties that hold in the framework of Picture Fuzzy Sets (PFS). Picture fuzzy sets extend classical fuzzy and intuitionistic fuzzy sets by incorporating an additional degree of neutrality, providing a more refined representation of uncertainty. We examine the validity of standard algebraic laws such as commutativity, associativity, distributivity, and idempotency under picture fuzzy operations, and identify the conditions under which these laws are preserved. The study contributes to a deeper understanding of the algebraic behavior of PFS and forms a theoretical basis for their further applications in fuzzy decision-making and information processing.]]>
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