Neutrosophic Algebraic Structures and Their Applications

Authors

Florentin Smarandache, University of New MexicoFollow
Memet Sahin
Derya Bakbak
Abdullah Kargın

Document Type

Book

Publication Date

2022

Abstract

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 our real world.

In classical algebraic structures, all operations are 100% well-defined, and all axioms are 100% true, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some operations or some laws.

Using the process of NeutroSophication of a classical algebraic structure we produce a NeutroAlgebra, while the process of AntiSophication of a classical algebraic structure produces an AntiAlgebra.

Publisher

Universidad Regional Autónoma de los Andes (UNIANDES)

Language (ISO)

English

Keywords

NeutroAlgebra, AntiAlgebra, NeutroStructure, AntiStructure

Recommended Citation

Smarandache, Florentin; Memet Sahin; Derya Bakbak; and Abdullah Kargın. "Neutrosophic Algebraic Structures and Their Applications." (2022). https://digitalrepository.unm.edu/math_fsp/563

Creative Commons License

This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 International License.