A10571291S52019

Fuzzy Soft Ternary Γ-Semirings-II
T. Satish¹, D. Madhusudhana Rao², P. Sivaprasad³, M. Vasantha^4
1T. Satish, Research Scholar, Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar (A.P), India.
²D. Madhusudhana Rao, Department of Mathematics, VSR & NVR College, Tenali, Guntur (A.P), India.
³P. Sivaprasad, Department of BSH, VFSTR’S University, Vadlamudi, Guntur (A.P), India.
⁴M. Vasantha, Department of Mathematics, DNR Engineering College, Bhimavaram, W.G. (A.P), India.
Manuscript received on 25 November 2019 | Revised Manuscript received on 19 December 2019 | Manuscript Published on 30 December 2019 | PP: 235-239 | Volume-9 Issue-1S5 December 2019 | Retrieval Number: A10571291S52019/19©BEIESP | DOI: 10.35940/ijeat.A1057.1291S519
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: In this paper we are introducing the notions of “fuzzy soft quasi T  -ideal(FSQTΓI), Fuzzy soft bi-T  – ideal(FSBTΓI)” are introduced. It is proved that (1) A “fuzzy soft set (q,P1, ) over a ternary Γ-semiring(TΓ-SR)”T is a FSQTΓI over T iff  a  P1, q(a)   is a “quasi-ideal of T”. (2) Every “Fuzzy soft left (right, lateral) T  – ideal[FSLTΓI(FSMTΓI, FSRTΓI)] over a TΓ-SR T is a FSQTΓI over T”: (3)Every “FSQTΓI is a fuzzy soft T  -SR over T”: (4) Let “(r,A,  ), (l,B,  ) and (m,C,  ) be FSLTΓI, FSMTΓI, FSRTΓI over T”, respectively. Then “(r,A,  )  (l,B,  )  (m,C,  ) is a FSQTΓI over T”. (5) Let “(f,A,  ) be a FSQTΓI and (g,B,  ) a Fuzzy soft ternary  – semiring(FSTΓSR) over T”. Then “(f,A,  ) R I (g, B,  ) is a FSQTΓI of (g, B,  )”. (6) Let “(f,A  ) and (g, B,  ) be two non-empty fuzzy soft sets over a TΓ-SR T”.Then the “fuzzy soft set (h, C,  ) = (f, A  )o(T, E,  ) o(g, B,  ) is a FSBTΓI over T”. Further many more properties are proved and some examples are given.
Keywords: TΓ-SR, FSTΓ-SR, FSTΓI, FSQTΓI.
Scope of the Article: Fuzzy Logics