This paper presents improvements to Zadeh's foundational work on fuzzy sets, focusing on the distributive law, convex combination, and convex fuzzy sets. Zadeh's 1965 paper introduced fuzzy sets, which have since become a cornerstone in handling vagueness and uncertainty. The authors highlight three key areas for improvement: the distributive law, convex combination, and convex fuzzy sets. For the distributive law, the paper revisits Zadeh's original proof and identifies cases where the original proof was incomplete. The authors provide a more comprehensive analysis by using mathematical expressions to verify the distributive law, showing that the original proof missed some cases. They also derive lemmas that help in proving the distributive law. In the context of convex combination, the paper points out that Zadeh's formula for the membership function of a convex combination is only valid when the membership functions of the fuzzy sets involved are different. When they are the same, the formula is not well-defined. The authors provide a revised formula that allows for a more general case. Regarding convex fuzzy sets, the paper notes that Zadeh's definition of convex fuzzy sets is incomplete. The authors provide a more comprehensive definition that covers all possible cases, ensuring that the set of points with membership greater than or equal to a certain value is convex. The paper concludes that these revisions enhance the understanding and application of fuzzy sets, providing a more robust mathematical foundation for practitioners in the field. The authors emphasize the importance of Zadeh's original work and the need for continuous refinement and improvement in the field of fuzzy set theory.This paper presents improvements to Zadeh's foundational work on fuzzy sets, focusing on the distributive law, convex combination, and convex fuzzy sets. Zadeh's 1965 paper introduced fuzzy sets, which have since become a cornerstone in handling vagueness and uncertainty. The authors highlight three key areas for improvement: the distributive law, convex combination, and convex fuzzy sets. For the distributive law, the paper revisits Zadeh's original proof and identifies cases where the original proof was incomplete. The authors provide a more comprehensive analysis by using mathematical expressions to verify the distributive law, showing that the original proof missed some cases. They also derive lemmas that help in proving the distributive law. In the context of convex combination, the paper points out that Zadeh's formula for the membership function of a convex combination is only valid when the membership functions of the fuzzy sets involved are different. When they are the same, the formula is not well-defined. The authors provide a revised formula that allows for a more general case. Regarding convex fuzzy sets, the paper notes that Zadeh's definition of convex fuzzy sets is incomplete. The authors provide a more comprehensive definition that covers all possible cases, ensuring that the set of points with membership greater than or equal to a certain value is convex. The paper concludes that these revisions enhance the understanding and application of fuzzy sets, providing a more robust mathematical foundation for practitioners in the field. The authors emphasize the importance of Zadeh's original work and the need for continuous refinement and improvement in the field of fuzzy set theory.