International Journal of Mathematics Trends and Technology
Volume 61 | Number 1 | Year 2018 | Article Id. IJMTT-V61P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P501
In this Paper the terms [𝑓), fuzzy left(right) identity, fuzzy left(right) zero of a posemigroup are introduced. It is proved that fuzzy left identity and fuzzy right identity of a posemigroup if it exists then both are same. Also proved that fuzzy left zero and fuzzy right zero of a posemigroup exists then both are equal. Next proved that intersection of arbitrary family of fuzzy posemigroups of a posemigroup S is a fuzzy posemigroup of S. Furthermore, proved that intersection of all fuzzy posemigroups of S containing f is ideal generated by fuzzy subset f. Next proved that f is a fuzzy ideal of a posemigroup S iff𝑓𝑜𝑆 ⊆ 𝑓, 𝑆𝑜𝑓 ⊆ 𝑓 and 𝑓 ⊆ 𝑓. Next demonstrate the union, intersection of arbitrary family of fuzzy ideals of posemigroup S is fuzzy ideal of S. Next proved that every completely prime fuzzy ideal is weakly completely prime fuzzy ideal. Also proved that if f is completely prime fuzzy ideal then 𝑓𝑡 is sub semigroup and completely prime ideal of S. Next proved that 𝑓𝑡 is completely prime ideal of S then f is weakly completely prime fuzzy and completely prime fuzzy ideal of S. Next proved that equivalent conditions of prime fuzzy ideal, f is prime fuzzy ideal iff 1-f is a fuzzy m-system of S if 1 − 𝑓 ≠ ∅. Finally proved that every maximal fuzzy ideal of S is a prime fuzzy ideal of S.
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RamyaLatha P, A. Gangadhara Rao, J.M.Pradeep, K.Aruna, "Fuzzy Identity, Fuzzy Zero of Po Semigroup and Completely Prime Fuzzy, Prime Fuzzy Ideal of Po Semigroup," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 1, pp. 1-9, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P501
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