Fuzzy Regular Subsemigroups of Partially Ordered Semigroups and Fuzzy Simple Partially Ordered Semigroups
Journal Title: International Journal of engineering Research and Applications - Year 2018, Vol 8, Issue 8
Abstract
In this paper the terms, fuzzy regular subsemigroup,λ-cut, fuzzy left regular subsemigroup, fuzzy right regular subsemigroup, fuzzy Intraregularsubsemigroup, fuzzy completely regular subsemigroup, ideal generated by the ordered fuzzy pointaλ , fuzzy semisimple, fuzzy left simple semigroup, fuzzy right simple semigroup, fuzzy simple semigroup, fuzzy globally idempotent, maximal fuzzy ideal in a posemigroup are introduced. It is proved that, if fis fuzzy regular subsemigroup of S thenfis 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 S is left (right) regular semigroup then aλ is fuzzy semisimple. It is proved that, If aλ is fuzzy intra regular semigroup then aλ is fuzzy semisimple. It is also proved that,f Sa and f aS is fuzzy left and fuzzy right ideals of S respectively. S is a fuzzy left (right) simple posemigroup if and only if f Sa = fS = S (f aS = fS = S) ∀a ∈ S. It is proved that for any semigroup S the following are equivalent.a)S is a left(right) simple posemigroup b) S is a fuzzy left( right) simple semigroup. Finally we proved that if S is a posemigroup with unity e then the union of all proper fuzzy idealsofSistheuniquefuzzymaximalidealofS. Mathematical Subject Classification:20m07, 20m11, 20m12
Authors and Affiliations
Ramyalatha P, A. Gangadhara Rao, J. M. Pradeep, A. Anjaneyulu
Keywords
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