International Journal of Mathematics Trends and Technology
Volume 60 | Number 4 | Year 2018 | Article Id. IJMTT-V60P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P536
In this paper the terms, fuzzy regularpo ternarysubsemigroup,๐-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 ๐๐ , 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 ๐๐ is fuzzy regular then ๐๐ is fuzzy semisimple. It is proved that, If an ordered fuzzy point ๐๐ of T is left( lateral ,right) regular poternarysemigroup then ๐๐ is fuzzy semisimple. It is proved that, If ๐๐ is fuzzy intra regularPOternary semigroup then ๐๐ is fuzzy semisimple. It is also proved that๐ ๐ก๐ก๐ , ๐ ๐๐ก๐ก are fuzzy left and fuzzy right ideals of T respectively then T is a fuzzy left (right) simple poternarysemigroup if and only if ๐ ๐ก๐ก๐ = ๐๐ก = ๐๐ ๐๐ก๐ก = ๐๐ก = ๐) โ๐ โ ๐. 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.
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J.M. Pradeep, A. Gangadhara Rao, A. Anjaneyulu, P. Ramyalatha, "Fuzzy Regular Ternary Sub Semi Group of a Partial Ordered Ternary Semi Group and Fuzzy Simple Partial Ordered Ternary Semi Groups," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 4, pp. 233-240, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P536
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