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In this paper, we introduce the notion of neutrosophic N -bi-ideal structure over a semigroup. We characterize semigroups, regular semigroups and intra-regular semigroups in terms of neutrosophic N -bi-ideal structures. We also show that the intersection of neutrosophic N -ideals and the neutrosophic N -product of ideals will coincide for a regular semigroup.
In this paper, we introduce the notion of neutrosophic ℵ-bi-ideal for a semigroup. We infer different semigroups using neutrosophic ℵ -bi-ideal structures. Moreover, for regular semigroups, neutrosophic ℵ-product and intersection of neutrosophic ℵ-ideals are identical.
We define the concepts of neutrosophic ℵ -interior ideal and neutrosophic ℵ −characteristic interior ideal structures of a semigroup. We infer different types of semigroups using neutrosophic ℵ-interior ideal structures. We also show that the intersection of neutrosophic ℵ-interior ideals and the union of neutrosophic ℵ-interior ideals is also a neutrosophic ℵ-interior ideal.
The objective of this paper is to extend the concept of neutrosophic N-ideals in semigroups to ternary semigroups and investigate some of its properties. Moreover, consider characterizations of neutrosophic N-left (resp., N-lateral, N-right) ideals by using the notion of neutrosophic N-products. Furthermore, we show that the homomorphic preimage and the onto homomorphic image of neutrosophic N-left (resp., N-lateral, N-right) ideals are also neutrosophic N-left (resp., N-lateral, N-right) ideals in ternary semigroups.
Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic biLA-semigroup,soft neutosophic sub bi-LA-semigroup, soft neutrosophic N -LA-semigroup with the discuission of some of their characteristics
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: Neutrosophic Soft Fixed Points, Selection of Alternative under the Framework of Single-Valued Neutrosophic Sets, Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem.
The topics discussed in this book are Int-soft semigroup, Int-soft left (right) ideal, Int-soft (generalized) bi-ideal, Int-soft quasi-ideal, Int-soft interior ideal, Int-soft left (right) duo semigroup, starshaped (∈, ∈∨ qk)-fuzzy set, quasi-starshaped (∈, ∈∨ qk)-fuzzy set, semidetached mapping, semidetached semigroup, (∈, ∈ ∨qk)-fuzzy subsemi-group, (qk, ∈ ∨qk)-fuzzy subsemigroup, (∈, ∈ ∨ qk)-fuzzy subsemigroup, (qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈ ∨ qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈, ∈∨ qkδ)-fuzzy subsemigroup, ∈∨ qkδ -level subsemigroup/bi-ideal, (∈, ∈∨ qkδ )-fuzzy (generalized) bi-ideal, δ-lower (δ-upper) approximation of fuzzy set, δ-lower (δ-upper) rough fuzzy subsemigroup, δ-rough fuzzy subsemigroup, Neutrosophic N -structure, neutrosophic N -subsemigroup, ε-neutrosophic N -subsemigroup, and neutrosophic N -product.
This volume is a collection of fourteen papers, written by different authors and co-authors (listed in the order of the papers): N. Radwan, M. Badr Senousy, A. E. D. M. Riad, Chunfang Liu, YueSheng Luo, J. M. Jency, I. Arockiarani, P. P. Dey, S. Pramanik, B. C. Giri, N. Shah, A. Hussain, Gaurav, M. Kumar, K. Bhutani S. Aggarwal, V. Pătraşcu, F. Yuhua, S. Broumi, A. Bakali, M. Talea, F. Smarandache, M. Khan, S. Afzal, H. E. Khalid, M. A. Baset ,I. M. Hezam.
This book consists of seven chapters. In chapter one we introduced neutrosophic ideals (bi, quasi, interior, (m,n) ideals) and discussed the properties of these ideals. Moreover, we characterized regular and intra-regular AG-groupoids using these ideals. In chapter two we introduced neutrosophic minimal ideals in AG-groupoids and discussed several properties. In chapter three, we introduced different neutrosophic regularities of AG-groupoids. Further we discussed several condition where these classes are equivalent. In chapter four, we introduced neutrosophic M-systems and neutrosophic p-systems in non-associative algebraic structure and discussed their relations with neutrosophic ideals. In chapter five, we introduced neutrosophic strongly regular AG-groupoids and characterized this structure using neutrosophic ideals. In chapter six, we introduced the concept of neutrosophic ideal, neutrosophic prime ideal, neutrosophic bi-ideal and neutrosophic quasi ideal of a neutrosophic semigroup. With counter example we have shown that the union and product of two neutrosophic quasi-ideals of a neutrosophic semigroup need not be a neutrosophic quasi-ideal of neutrosophic semigroup. We have also shown that every neutrosophic bi-ideal of a neutrosophic semigroup need not be a neutrosophic quasi-ideal of a neutrosophic semigroup. We have also characterized the regularity and intra-regularity of a neutrosophic semigroup. In chapter seven, we introduced neutrosophic left almost rings and discussed several properties using their neutrosophic ideals. Keywords: neutrosophic set, algebraic structure, neutrosophic ideal, AG-groupoids, neutrosophic minimal ideals, neutrosophic regularities, neutrosophic M-systems, neutrosophic p-systems, neutrosophic strongly regular AG-groupoids neutrosophic prime ideal, neutrosophic bi-ideal, neutrosophic quasi ideal, neutrosophic semigroup, neutrosophic left almost rings
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.