Mumtaz Roshan Ali
580 California St., Suite 400
San Francisco, CA, 94104
Soft neutrosophic semigroups and their generalization
2013, viXra
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Abstract
Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly dened objects. In this paper we introduced soft neutrosophic semigroup,soft neutosophic bisemigroup, soft neutrosophic N-semigroup with the discuissionf of some of their characteristics. We also introduced a new type of soft neutrophic semigroup, the so called soft strong neutrosophic semigoup which is of pure neutrosophic character. This notion also foound in all the other corresponding notions of soft neutrosophic thoery. We also given some of their properties of this newly born soft structure related to the strong part of neutrosophic
References (26)
- Their AN D operation (F, A) ∧ (K, B) is soft neutrosophic strong bisemigroup over BN (S).
- Their OR operation (F, A) ∨ (K, B) is not soft neutrosophic strong bisemigroup over BN (S). Definition 4.2. Let (F, A) and (H, B) be two soft neutrosophic strong bisemigroups over BN (S). Then (H, B) is a soft neutrosophic strong subbisemigroup of (F, A), if 1. B ⊂ A.
- H(x) is neutrosophic strong subbisemigroup of F (x), for all x ∈ B. Example 4.2. Let BN (S) = {0, 1, 2, I, 2I, Z ∪ I , ×, +} be a neutrosophic bisemigroup.
- Let T = {0, I, 2I, 2Z
- ∪ I , ×, +} and R = {0, 1, I, 4Z ∪ I , ×, +} are neutrosophic strong subbisemigroups of BN (S) . Then (F, A) is soft neutrosophic strong bisemigroup over BN (S), where F (x 1 ) = {0, I, 2I, 2Z ∪ I , ×, +}, F (x 2 ) = {0, I, 4Z ∪ I , ×, +}. Then (H, B) is a soft neutrosophic strong subbisemigroup of (F, A), where H (x 1 ) = {0, I, 4Z ∪ I , ×, +} . Theorem 4.2. Let (F, A) be a soft neutrosophic strong bisemigroup over BN (S) and {(H i , B i ) ;
- i ∈ I} be a non empty family of soft neutrosophic strong subbisemigroups of (F, A) then
- ∩ i∈I (H i , B i ) is a soft neutrosophic strong subbisemigroup of (F, A).
- ∧ i∈I (H i , B i ) is a soft neutrosophic strong subbisemigroup of ∧ i∈I (F, A). Florentin Smarandache Neutrosophic Theory and Its Applications. Collected Papers, I References
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