Abstract
In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, <i>τ</i>-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the new theorems and related properties of above mention notions with respect to PU-new ideal on PU-algebras. Such that for (Ⱬ,<i> τ</i>) to be a TSFP on Ⱬ and the set Ḟ is a fuzzy in Ⱬ and N<SUB>Ḟ</SUB> be a fuzzy neighborhood system of Ḟ then the finite intersection of elements of ‘N<SUB>Ḟ</SUB>’ is also an element of ‘N<SUB>Ḟ</SUB>’ also any fuzzy set of Ⱬ which contains an element of “N<SUB>Ḟ</SUB>” is also an element of “N<SUB>Ḟ</SUB>”. Furthermore we prove the conditions with respect to fuzzy neighborhood, convergence of a sequence of fuzzy sets, fuzzy interior set of a fuzzy set under which a fuzzy set <I>Ḟ</I> is <i>τ</i>-open. We show that how the function Ψ from (Ⱬ<sub>1</sub>,<i>τ</i>) to (Ⱬ<sub>2</sub>,ω) is fuzzy continuous. We prove that if Ψ is a fuzzy continuous function then for every fuzzy set <I>Ḟ</I> in Ⱬ<sub>1</sub>, inverse of each neighborhood of Ψ(<I>Ḟ</I>) is a neighborhood of a fuzzy set <I>Ḟ</I>.
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