Fuzzy Soft Ternary Γ-Semirings-II
T. Satish1, D. Madhusudhana Rao2, P. Sivaprasad3, M. Vasantha4
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