Abstract

In this paper the terms, fuzzy regularpo ternarysubsemigroup,𝜆-cut, fuzzy left regularTernary posubsemigroup, fuzzy right regularpoternary subsemigroup, fuzzy Intra regular po ternary subsemigroup, fuzzy completely regularpo ternary subsemigroup, ideal generated by the ordered fuzzy point 𝑎𝜆 , fuzzypoternarysemisimple, fuzzy left simplepoternarysemigroup, fuzzy right simplepoternary semigroup, fuzzy simplepoternary semigroup, fuzzy globally idempotent, maximal fuzzy ideal in a po ternarysemigroup are introduced. It is proved that, if f is fuzzy regular POternary subsemigroup of T then f is fuzzy idempotent. It is proved that, If f is fuzzy completely regular then f is regular, left regular and right regular. It is proved that, If 𝑎𝜆 is fuzzy regular then 𝑎𝜆 is fuzzy semisimple. It is proved that, If an ordered fuzzy point 𝑎𝜆 of T is left( lateral ,right) regular poternarysemigroup then 𝑎𝜆 is fuzzy semisimple. It is proved that, If 𝑎𝜆 is fuzzy intra regularPOternary semigroup then 𝑎𝜆 is fuzzy semisimple. It is also proved that𝑓 𝑡𝑡𝑎 , 𝑓 𝑎𝑡𝑡 are fuzzy left and fuzzy right ideals of T respectively then T is a fuzzy left (right) simple poternarysemigroup if and only if 𝑓 𝑡𝑡𝑎 = 𝑓𝑡 = 𝑇𝑓 𝑎𝑡𝑡 = 𝑓𝑡 = 𝑇) ∀𝑎 ∈ 𝑇. It is proved that for anypo ternary semigroup T the following are equivalent(.a)Tis a left( lateral, right) simple po ternarysemigroup(b) T is a fuzzy left( lateral, right) simple po Ternary semigroup. Finally we proved that if T is a po ternarysemigroup with unity e then the union of all Proper fuzzy idealsofTistheuniquefuzzymaximalidealof T.

Keywords

References

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