Open AccessFuzzy Soft Ternary Γ-Semirings-II
Publication year - 2019
Publication title -
international journal of engineering and advanced technology
Language(s) - English
Resource type - Journals
ISSN - 2249-8958
DOI - 10.35940/ijeat.a1057.1291s52019
Subject(s) - ideal (ethics) , semiring , mathematics , fuzzy logic , ternary operation , combinatorics , discrete mathematics , computer science , artificial intelligence , philosophy , epistemology , programming language
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.