In this paper, we define a normal fuzzy PS-sub algebra, Normal fuzzy PS- ideal , maximal element and discussed some of their properties in detail. The concept of fuzzy set was initiated by L.A.Zadeh in 1965 [7]. It has opened up keen insights and applications in a wide range of scientific fields. Since its inception, the theory of fuzzy subsets has developed in many directions and found applications in a wide variety of fields. The study of fuzzy subsets and its applications to various mathematical contexts has given rise to what is now commonly called fuzzy mathematics. Fuzzy algebra is an important branch of fuzzy mathematics. Fuzzy ideas have been applied to other algebraic structures su
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