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Neutrosophic Algebraic Structures And Their Applications, Florentin Smarandache, Memet Sahin, Derya Bakbak, Abdullah Kargın

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Logic is a general framework for unification of many existing logics, such as fuzzy logic (especially intuitionistic fuzzy logic), paraconsistent logic, intuitionistic logic, etc.

In 2019 Smarandache generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false}, and he continued to develop them and extend a Structure in any field to the NeutroStructure and AntiStructure.

The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from …

Neutroalgebra Theory, Vol. I, Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargın

Branch Mathematics and Statistics Faculty and Staff Publications

In general, in any field of knowledge, with respect to any structure, one has the following neutrosophic triplet . They were introduced by Smarandache in 2019 and 2020.

1) A classical Structure is a structure whose all elements are characterized by the same given Relationships and Attributes and Laws.

2) A NeutroStructure is a structure that has at least one NeutroRelation or one NeutroAttribute or one NeutroLaw, and no AntiRelation and no AntiAttribute and no AntiLaw.

3) An AntiStructure is a structure that has at least one AntiRelation or one AntiAttribute or one AntiLaw.

As a particular case, in the …