Fuzzy Regular Ternary Sub Semi Group of a
Partial Ordered Ternary Semi Group and
Fuzzy Simple Partial Ordered Ternary Semi
Groups

J.M. Pradeep; A. Gangadhara Rao; A. Anjaneyulu; P. Ramyalatha

doi:https://doi.org/10.14445/22315373/IJMTT-V60P536

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 4 | Year 2018 | Article Id. IJMTT-V60P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P536

Fuzzy Regular Ternary Sub Semi Group of a Partial Ordered Ternary Semi Group and Fuzzy Simple Partial Ordered Ternary Semi Groups

J.M. Pradeep, A. Gangadhara Rao, A. Anjaneyulu, P. Ramyalatha

Citation :

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

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

Fuzzy regularpoternarysubsemigroup,fuzzy completely regular poternarysubsemigroup,fuzzy Intra regular poternarysubsemigroup, fuzzy semisimple, fuzzy globally idempotent.

References

[1] ANJANEYULU A., Structure and ideal theory of semigroups – Thesis, ANU (1980).
[2] Clifford A.H and Preston G.B., The algebroic theory of semigroups ,vol – I American Math. Society, Province (1961).
[3] Clifford A.H and Preston G.B., The algebroic theory of semigroups ,vol – II American Math. Society, Province (1967).
[4] LJAPIN E. S., Semigroups, American Mathematical Society, Providence, Rhode Island (1974).
[5] Petrch.M., Introduction to semigroups ,Merril publishing company, Columbus, Ohio (1973).
[6] P.M.Padmalatha and A.GangadharaRao, Simple partially ordered semigroups, Global Journal of Pure and Applied Mathematics, Volume 10,, Number 3(2014).
[7] W.M.Wu, Normal fuzzy subsemigroups, Fuzzy Math1(1).21-30(1981)
[8] T.M.G.Ahsanullah and F.A. AI-Thukair, Conditions on a semigroup to be a fuzzy neighborhood group, Fuzzy Sets and Systems, 55(1993), 333-340.
[9] J.N.Mordeson, D. S. Malik, N. Kuroki, Fuzzy Semigroups Springer-Verlag Berlin Heidelberg GmbH ISBN 978-3-642-05706-9 ISBN 978-3-540-37125-0 (eBook) DOI 10.1007/978-3-540-37125-0
[10] Xiang-Yun Xie,, Jian Tang, Fuzzy radicals and prime fuzzy ideals of ordered semigroups, Information Sciences 178 (2008), 4357– 4374.
[11] N.Kehayopulu,M.Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum 65(2002), 128-132
[12] Jizhongshen,On fuzzy Regular Subsemigroups of a semigroup, Information Sciences 51,111-120(1990)