Abstract
Shal et. al cite:SKR, have introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring. In this paper, we investigate the concept of intuitionistic anti fuzzy normal subrings over non-associative rings and give some properties of such subrings
Highlights
In 1972, ageneralization of commutative semigroups has been established by Kazim et al [9]
A ∩ B is an LA-subring of an left almost ring (LA-ring) R1 × R2 × ... × Rn if and only if the intuitionistic anti characteristic function χZ = μχZ, γχZ of Z = A ∩ B is an intuitionistic anti fuzzy normal LA-subring of an LA-ring R1 × R2 × ... × Rn
A1 × A2 × ... × An is an LA-subring of an LA-ring R1 × R2 × ... × Rn if and only if the intuitionistic anti characteristic function χA = μχA, γχA of A = A1 × A2 × ... × An is an intuitionistic anti fuzzy normal LA-subring of an LA-ring R1 × R2 × ... × Rn
Summary
In 1972, ageneralization of commutative semigroups has been established by Kazim et al [9]. Shal et al [17], introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring (LA-ring). We define the direct product of intuitionistic fuzzy sets A1 and A2 of LA-rings R1 and R2, respectively and investigate the some basic properties of intuitionistic anti fuzzy normal LA-subrings of an LA-ring R1 × R2. We define the direct product of intuitionistic fuzzy sets A1, A2, ..., An of LA-rings R1, R2, ..., Rn, respectively and examine the some fundamental properties of intuitionistic anti fuzzy normal LA-subrings of an LA-ring R1 × R2 × ... × Rn. Let A and B be intuitionistic fuzzy sets of LA-rings R1 and R2 with left identities e1 and e2, respectively and A × B be an intuitionistic anti fuzzy normal LA-subring of an. If μB (x) ≥ μA (e1) and γB (x) ≤ γA (e1) , for all x ∈ R2, B is an intuitionistic anti fuzzy normal LA-subring of R2
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